## Rational Expressions Questions and Answers

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Which statement does not describe the graph of 2 / {x - 3}? a) Function is undefined when x = 3, so it has a vertical asymptote at x = 3. b) The graph has an axis of symmetry. c) The graph has a ho...

Graph the rational function f (x) = {-5} / {-x + 5}.

The graph of the rational for Function. R (x) = \frac{x^2 + x - 12}{x^2 - x - 6}

Determine the following. Be sure to check your answers with the calculator. Let h(x) = \frac{31x - 6}{x + 4}. Evaluate h(6). Determine x when h(x) = 21.

Determine the following. Be sure to check your answers with the calculator. Let f(x) = \frac{-30}{x - 10}. Evaluate f(4). Determine x when f(x) = 5.

Simplify. {x^2 + 2 x - 63} / {x^2 + 3x - 70} multiplied by {x^2 - 6x - 40} / {x^2 + 13 x + 36}

A rational function f(x) contains quadratic functions in both the numerator and denominator. Also, the function f(x) has a vertical asymptote at x=5, a single x-intercept of (2,0) and f is removabl...

Find the domain of , given f(x) = 2x - 5 and g(x) = \sqrt{x + 4}

Graph g(x) = 5x/(x^2 - 9). Include all asymptotes and intercepts.

Find the horizontal asymptote, if any, of the graph of the rational function g(x) = \dfrac{16x^2}{8x^2 + 5}

Find the domain of the following rational function. H(x) = \dfrac{-9x^2}{(x - 4)(x + 2)}

Find the domain of the following function: f(x)= \dfrac{1}{3x-2}

On the same axes, sketch the curves of the rational functions (a) i. f(x) = x(x - 2)/(x - 1)^2 ii. g(x) = 1/(1 - x) Include all intercepts, asymptotes, holes and points where f(x) and g(x) interse...

For the function f(x) = 3/(x + 8), find f(p).

Find all vertical asymptotes and create a rough sketch of the graph near each asymptote for the function f(x) = (x +4)/(x^2 - 16).

The function h is defined below. h(x) = \frac{x - 6}{x^2 + 6x + 5} Find all values of x that are NOT in the domain of h. If there is more than one value, separate them with commas. x = \boxed{\space}

Graph the function y = \frac{x^2 4x 12 }{ 2x^2 8 } .

a) Sketch the graph of y = (x - 1)^2(x + 3)(x - 2)^2 b) sketch the graph of y = \frac{(2x^2 - 11x +12)}{(x^2 - x - 20)}

Determine the domain and range of the function: f(x) = 3/(x - 2) + 1.

Evaluate an expression when x = 1, y = 3, z = 5. (x^2 + z)/(y^2 + 2z)

Determine the domain of the following functions. Write your answer in interval notation. f(x) = \sqrt{5 - 4x}

Consider the following function. f(x) = square root {8 - e^{2 x}} (a) Find domain of f. (Enter your answer using interval notation.) (b) Find f^{-1}.

Find all numbers not in the domain of the function. f(x) = \frac{x^{2} - 4}{x^{2} + 3x - 28} A) -7,4 B) 2,-2 C) 7,-4 D) 0

Determine the domain and range of the function: f(x) = \frac{3}{x - 2} + 1

Find the domain of the function. (Enter your answer using interval notation. )

Is the function f(x) = \frac{1}{x} an exponential function? If so, explain why.

Given f(x) = {1}/{x-2}. Find f(1).

Write as a single rational expression: \frac{2x^{2}}{5ab} + \frac{a^{2}u^{2}}/{10b^{3}k}

Find the domain of the 4th root of (1 - x^2).

Find the difference quotient \frac{f(x + h) - f(x)}{h}, h is not equal to 0. f(x) = 7x - 9

Find all numbers for which the rational expression is undefined 8/(x - 4).

Find one application of a rational function in a real-world situation. Thoroughly describe the application, including the rational equation used.

Find the horizontal and oblique asymptotes, if any, for the given rational function G(x)=(x^4-1)/(3x^2-3x).

How to solve the following problem? 8/(x^2 - 16) + 3/4 = 1/(x - 4).

How do the following equations look differently when graphed? Explain. y = sqrt x + 3 and y = 2sqrt x + 3.

Simplify. \sqrt[3]{-54x^{6}y^{4}}

Find the inverse of the following function. Find the domain, range, and asymptotes of each function. f(x)=3+ln(x+2)

Evaluate the function f(x) at the given numbers (correct to six decimal places). f(x) = \frac{x^2 - 8x}{ x^2 - 7x - 8 }, x = -0.95, -0.99, and -0.999

True or False? A singularity of a rational function is either removable or is a pole.

Sophia plots points on a graph to represent the shape of a concave lens. Which type of function should Sophia use to model the shape of the lens; linear, exponential, quadratic, or square root?

Create a function that has a graph with the following features: * Two vertical asymptotes at x=1 \text{ and } x=3 . * One horizontal assymptote at y = 1 . * x intercepts at...

Find all asymptotes of indicated type. f(x) = (x - 9)/(x^2 - 4); vertical.

What is the graph of the raional function y= (x-4)(x-1)/(x+5)(x-5)?

The rational function g(x) = (x^2 - 4x)/(x^2 - x - 20) has a hole at (blank).

Find the horizontal and oblique asymptotes for the rational function, G(x)=\frac{(x^{4} - 1) }{(3x^{2} - 3x)}.

Find all numbers for which the rational expression is undefined. r^3-8r/r^2-25

What are the points of discontinuity: y = (x - 2)/(x^2 + 5x - 6)?

Find f(9) if f(x)=\frac{4}{x - 9}.

Which numbers need to be excluded from the domain of the function y = 4/(x - 6) + 3/(x + 5)?

state the vertical, horizontal asymptotes and zeros of the rational function, f(x) = x^2+3x+2/ x^2+5x+4 . why is there no zero at x = 1?

Is y = sqrt 2x a function?

What is the range of the function defined by f(x) = 1/(x + 2)?

Sketch a graph of the most general polynomial function that satisfies the given conditions: degree = 3; has a zero of 3 with multiplicity 2; leading coefficient is positive.

What is the product in simplest form state any restrictions on the variable \frac{4a^5}{7b^6}?

Given f(x)= x^3 - 2x^2 + 6. a. Graph the function by making a table of values. b. Determine consecutive values of x between where each real zero is located. c. Estimate the x-coordinates at which...

Find a rational function that satisfies the given conditions. Vertical asymptotes x = -4 and x = 5; x-intercept (-2, 0)

Sketch the level curve of f(x,y) = \frac{y}{x^2 + y^2}

Find the Domain and Range for y = \frac{1}{-x -2} and y = \frac{-4}{x-4} + 4.

Find a rational function that satisfies the given conditions. Answers may vary, but try to give the simplest answer possible: Vertical asymptotes x = -4, x = 5; x-intercept (-2, 0)

Sketch the curve of function y = \frac{x-1}{x^2-x-6}.

Determine the equations of the asymptotes: g(x) = (2x^2 + 1) / (x+3).

Find the oblique asymptote for the given function. y = 2x^2 / (x + 1).

Find the vertical and horizontal asymptotes for the given function. y = (2x^2 + 8) / (x^2 - 9).

Find the vertical and horizontal asymptotes for the given function. y = 3x / (2x^2 + 1).

Find the vertical and horizontal asymptotes for the given function. y = 5x / (x-1).

Which is a rational function? (a) y = x^2 -3x + 5. (b) y = x - 5 / x. (c) y= square root (x - 3). (d) y = 5.

The rational function g(x) = \frac{x^2 - 4x}{x^2 - x - 20} has a hole at?

Find all numbers for which the rational expression is undefined: \frac{r^{2} - 4r}{r^{2} - 4r}

Determine the values of x for which the expression is undefined. \frac{1}{2x^2 - 50}

Given f(x)=rootsignx-2 and g(x) = x-7 what is the domain of the quotient function? A. (-infinity,2] B. )-infinity,7 U (7, infinity) C. [2,7) U (7, infinity) D. (2,infinity)

What are rational expressions? Why must we always be mindful of the final value of the denominator in a rational expression? For example, consider the rational expression 3x/(x2-16) . What values...

Determine the domain of f(x)= \frac{(x + 2}{(x - 6)} without graphing.

Graph all vertical and horizontal asymptotes of the function f(x)= 3x2 + 6x - 9/ x2 - 4.

For what values of x is the following expression: \frac{1}{(x^2 - 25)}. How do you solve and determined the undefined value?

For what value of x is the rational expression below equal to zero? \frac{x-8}{x+8}.

Find the domain of the function g(x) = \frac{3}{10 - 7x}.

Find the domain of the function. Make sure answer is in interval notation. f(x) = 5x\sqrt{x - 2}

Explain how to graph rational expressions that have vertical and horizontal asymptotes.

Find the domain of the following: f(x) = \frac{3}{x-7}

Multiply the following rational expressions and simplify the result. \frac{5y^2}{5y^2+30y-35}.\frac{2y^3+30y^2+112y}{8y+44} Which values of y make the resulting expression undefined? Choose all ans...

Why do some rational functions go through the horizontal asmyptote?

How do you find a hole in a rational function graph?

Where defined, \frac{sin^2(\theta)}{cos^2(\theta)} = 1?

Why is a rational function, not a transcendental function?

How to determine the end behavior of a rational function?

How to you find the restrictions of a rational expression?

A positive number n is a fraction less than one. Twice n plus the reciprocal of n equals 3. What is the value of n?

Explain how to find inverse of a rational function.

Use transformations to graph f(x) = 3e^{-x -2}

If f(x) = \frac{x^{2} - 9x}{x - 9} and g(x) = x, is it true that f = g?

Let f(x)= frac{x^2+4x+3}{x+1} A student recognizes that this function can be simplified as follows: f(x)=frac{x^2+4x+3}{x+1} = frac{(x+1)(x+3)}{x+1} = x+3 Since y = x+3 is a line with slope 1,...

Let P and Q be polynomials. Find \lim \limits_x \to \infty} \frac {P(x)}{Q(x)} if the degree of P is a. less than the degree of Q, b. greater than the degree of Q.

Given the rational function. f(x)= \frac {3x+4}{-5x+8}. Determine the following: a. Where the vertical asymptote occurs? b. At what point x intercept occurs? c. At what point y intercept occurs?...

Draw the graph for the following function: f(x)= \frac{2-x}{3+x}

Solve the following rational equations. a) \frac{1}{3a + 18} = 1 - \frac{8}{a + 6} b) \frac{7}{2x^2 - x - 1} = \frac{5}{x - 1}

Let f(x) \frac{2x^2-4}{x^2-3}. a. State the y intercept b. State the x intercept(s) c. State the vertical asymptote(s) d. State the horizontal asymptote

Find the partial fractions decomposition and an antiderivative. \frac{x + 2}{x^3 + x}

Suppose that in order to remove x% of the pollution from the oil spill, it costs C(x) = \frac{15x}{100-x} thousands of dollars. a. How much does it cost to remove 25% of the pollution? b. How...

Simplify the following. y = \frac{x}{4 - \sqrt{16 + x})}

For the given rational function f(x) = \frac{x^2-x+6 }{x^2-2x-3} \\ a) Find the domain of f. \\ b) Identify any vertical asymptotes of the graph of y=f(x). \\ c) Identify any holes in the graph....

Let f(x) = \frac{3x - 9}{x - 2} (a) state the domain (b) state the vertical asymptote(s) (c) State the horizontal asymptote (d) state the graph

Solve. x^\frac{-1}{2}(x + 9)^\frac{1}{2} + x^\frac{1}{2}(x + 9)^\frac{-1}{2}

What is the domain and range, x- and y-intercept, and horizontal and vertical asymptote of y = \frac{400 + 40x}{x}?

Which is a rational function? a) Y = \frac{x - 3}{x^2} \\ b) Y = 2x \\ c) Y = \frac{x - 5}{2} \\ d) Y = x^2 - x + 4

Draw a rough picture of the following surface and also clarify some basic geometric properties (e.g. axis, vertex): x^2 + 2z^2 - y^2 = 1.

Draw a rough picture of the following surface and also clarify some basic geometric properties (e.g. axis, vertex): x^2 + z^2 = 4.

How would you explain to a seventh-grader the difference between the domains of an odd root radical function and an even root radical function? How would you change your explanation for someone who...

Find the domain of the real valued rational function f given below. f(x) = \frac{(x - 1) }{ (x - 3)}

How do you write the domain of a rational function in interval notation?

Find the problem in the following equation (x^2 + x-6)/(x - 2) = x + 3

Maria bought seven boxes. a week later half of all her boxes were destroyed in a fire. there are now only 22 boxes left. with how many did she start with?

The formula T= 2pi sqrt(L / 980) can be used to find the period (T in seconds, the time it takes a pendulum to complete one cycle) of a pendulum that is L cm long. (a) Rewrite this formula using ra...

Find all numbers for which the rational expression is undefined. \frac{7}{3v + 7}

Simplify and find the excluded values. \frac{15x^2}{15x + 10}

Find the excluded value for the following. \frac{12a}{a^2 - 3a - 10}

(a) What is wrong with the following equation? x^2 + x - 6/x - 2 = x + 3 (b) In view of part (a), explain why the equation lim x -> 2 (x^2 + x - 6/x - 2) = lim x -> 2 (x+3) is correct.

How can you tell whether a function is rational or not? How do you determine holes of a graph?

Find the domain and range of the function. f(x) = \frac{1}{(x - 1)^2} - 5

If f(x)= p(x) \ / \ q(x) and period of p(x) \text{ is } T_1 \text{ and period of } q(x) \text{ is } T_2 then find the period of f(x) .

List all asymptotes (both horizontal and vertical) of the rational function: f(x) = \frac{10x - 3}{8 - 7x}

What numbers for which the rational expression is undefined? \frac{8}{9x + 7}

Find the excluded value of the fraction. \frac{x + 11}{3x^2 + 5x - 2}

Complete the operation indicated. \frac{\frac{3}{s + 4}}{\frac{4}{5s}}

What is the range of the function r(x) = 1/(1 - x)^2? Express your answer in interval notation.

Let f(x) =(x+3)/(2x-5) Find the inverse function of f. What is the domain of f? What is the domain of the inverse function?

Write a complete approach statement for y = fraction {(2x + 1)(2 - x)}{2x + 1}.

Let f (x)= 2-x/3+x (a) State the domain. (b) State the vertical asymptote(s). (c) State the horizontal asymptote. (d) State the y-intercept. (e) State the x-intercept(s).

A certain factory, the daily output is Q(K,L)=60K^{1/2}L^{1/3} units, where K denotes the capital investment measured in units of $1,000 and L the size of the labor force measured in worker-hours....

Find the following quotient: {36 x^2 - 49 y^2}/ {6 x + 7 y}.

Create a function with the following properties: a. It has a horizontal asymptote at y= 2. b. It has a discontinuity at x= 2 which is not a vertical asymptote. c. It has no other discontinuities o...

Simplify the rational expression. State any excluded values. \frac{7x - 14}{x - 2} A. x B. 7; where x is not equal to -7 C. 7; where x is not equal to 2 D. 0

Let f(x) = (x)/(x^2-4) (a) State the y-intercept. (b) State the vertical asymptote(s). (c) State the horizontal asymptote.

Sketch the graph of F(x)=\frac{x^2}{x-1} . Identify asymptotes, extrema, points of inflection and / or axis intercepts.

What is the undefined value of { \frac{(3b^2 + 13b + 4)}{(b + 4)} }

Find all the numbers for which the rational expression is undefined { \frac{s^3-6x}{ s^2-9} }.

Is the following statement true or false: Polynomials and radical expressions differ because radical expressions contain rational numbers as exponents and polynomials do not.

A vehicle uses 1 tablespoon of gasoline to drive 125 yards. How many miles can the vehicle travel per gallon? Round your answer to the nearest mile. (Hint: There are 256 tablespoons in a gallon)

State any restrictions on the variables. { \frac{3y^2 - 3y}{ y - 3} }

Describe the transformation done by { y = \frac{1}{x} } to get { y = \frac{1}{4x -12} }

What are the excluded values of the function? y=\frac{5}{(6x-72)}

Find the possible formula for the function in the figure below. (Graph)

Find: 1. The graph of f is given. State the numbers at which f is not differentiable. Image src='annotation_2019-07-31_1518081039845790348880442.png' alt='' caption='' 2. Use the given graph to est...

1. If f(x) =\frac{x^2+1}{x^2-1}, find the value(s) of x where the graph of f has a horizontal tangents. 2. Prove the quotient rule using the product rule and the chain rule. 3. Simplify the follow...

Write an equation for the function graphed below.

Make a complete graph of f(x) = \frac{x^2}{x+3}

Find all discontinuities of the function g(x) = \frac{2x^2 - 14x + 24}{3x^2 - 6x - 9} . Use limits to determine what type each discontinuity is.

Consider the function f(x) = \frac{x^2}{(x-2)^2} a. Find the horizontal and vertical asymptotes. b. Find the intervals of increase and decrease. c. Find the intervals where the function is conca...

Write the function with a hole at x = 4 , a horizontal asymptote at y = 2 , and a vertical asymptote at x = - 1

Let f(x) = frac{40x^2 - 2x + 1}{x^3 - 3x^2 + 2x} . Find the domain of f(x) . Find the horizontal and vertical asymptotes.

Determine, with reason, if each statement is true or false. (a) The function {x^4 + x - 1} / {x^3 - 4 x + 9} is a proper rational function. (b) The polynomial x^3 + 5 x^2 + 4 x has only simple, lin...

Let \ f'(x) = \frac {-1(x+3)(x-1)}{(x+4)} Find all intervals for which f is increasing. Label the x-value for all relative extreme.

Where is the following function continuous? Be explicit and precise .Show the algeberic steps. f(x)=\frac{x}{x^2-1}

Is the integral of a rational function always a rational function?

Sketch the function f(x) = x \sqrt{2+x} Investigate the following graphical information a. Domain b. Intercepts c. Symmetry d. Asymptotes e. Concavity and points of inflection

Analyze and sketch the graph of f(x)=\frac{3x}{x^2-1}.

Sketch a graph of the function. List any extrema, and indicate any asymptotes or points of inflection. f (x) = {x + 1} / {x - 2}.

Analyze and sketch a graph of the function f(x) = fraction {x}{x+1}

Let f(s) = \frac{s + 1}{s^2} . Evaluate each of the following: a. f(2) = b. f(-2) = c. f(-x) = d. f(s + h) = e. f(s) + h =

Find all the vertical and horizontal asymptotes, maximum and minimum, and points of inflection of the graph and sketch the graph.

Use a graphing utility with the specified viewing window to find the points of intersection of the graphs of the following functions. f(x) = 5x - 1, g(x) = x^2 - 2; [-4, 9]\; \text{by}\; [-6, 30] S...

How do you find the vertical asymptotes of a rational function when the denominator is in factored form?

Graph f(x) = \frac{5x}{x^2 - 25} and indicate: a) the domain b) the intercepts and asymptotes c) where the function is increasing and decreasing d) intervals of local maximum and local minimum e) wh

Find all the vertical and horizontal asymptotes of the function f(x) = \frac{x^2 - 4}{3x^2 + 3x - 6}

Find the domain of the function and identify any vertical and horizontal asymptotes. f\left ( x \right ) \ = \ \frac{2x^{2}}{x \ + \ 6}

Consider the functions f(x) = \ln \frac{\sqrt {x^2+1}}{x} and g(x) = \frac{1}{2} \ln(x^2 + 1) - \ln(x) . Graph f and g. What is the relationship between the graphs and therefore between the funct...

Let f(x) =\frac{5x^2 + 1}{4 - x^2}. Determine the vertical and horizontal asymptotes of f.

Let f(x) = x^2 and g(x) = x^3. Use these graphs to sketch the graph of the following functions. A) h(x) = -(x - 1)^2 + 2 B) p(x) = (3 - x)^3 - 4

Graph the function: f(x)=\frac{3x^2+4x}{ 2x^2- 1}

Make a complete graph of f. f(x) = x^2/(x - 10).

Find a formula for a function f that satisfies the following conditions. \lim_{x \rightarrow \pm\infty},f(x)=0\lim_{x \rightarrow 0 },f(x)=-\infty, \\ , \\ \lim_{x \rightarrow 9^{-}},f(x)=\inft...

In 1774, Captain James Cook left 10 rabbits on a small Pacific island. The rabbit population is approximated by P(t)= \frac{2000}{1 + e^{5.3 - 0.4t}} with t measured in years since 1774. Use a calc...

What is wrong with the following equation? \frac{x^2 + x - 20}{x - 4} = x + 5 a. (x - 4) (x - 5) \neq x^2 + x - 20 b. The left-hand side is not defined for x = 0, but the right-hand side is...

Given f(x) = \frac{3x^2 - 5}{(x^3-5x+1)^2} You can check that on the interval (2,3) the function is never negative.

Consider the following. \\ g(x) = \frac{x^2 - x -6}{x^2 - 16}\\ (a) State the domain of the function.\\ (b) Identify all intercepts. \\ (c) Find any vertical and horizontal asymptotes.

The graph of a function f is shown below. A(x) = \int_1^x f(t) dt a. Graph y = A(x) for 1 \leq x \leq 5. b. Estimate the values of A(1), A(2), A(3), and A(4).

Another model of population growth that has been used to model salmon is the Bcvcrton-Holtz model given by f(x) = \frac{rx}{1+\frac{x}{b}} where r and b are positive constants. a. Find \lim_{x \...

Consider the function h(x) = \frac{x^2-9}{x^2-4} . a. Find the domain of h(x) . b. Find the x- and y- intercepts. c. Is h(x) even or odd ? d. Find the horizontal and vertical asymptotes.

Sketch the graph of f(x) = 1 - \frac{2x}{(x - 3)^2} close

At what points is the function y = \frac{x + 9}{x^2 - 14x + 45} continuous? Describe the set of x-values where the function is continuous, using interval notation.

Consider f(x) = \frac{2x^2 - 8}{x^2 - 5x - 6} \\ (a) Find the domain for this function.\\ (b) Find the x - and y-intercepts.\\ (c) Find the horizontal and vertical asymptotes.

Consider the function below. f (x) = \frac{x^2}{x^2 - 16} (a) Find the vertical and horizontal asymptotes. (b) Find the interval where the function is Increasing. Find the interval where the f...

Expand f(x) = \frac {1}{(3 - x)^3}.

Use the function below to answer the following questions. f(x) = (x^2 - 9)/(x - 3). (a) Determine the domain of the function, f. (b) Determine the value of f(3), if it exists.

Identify the extent, leading coefficient, and constant coefficient in the following polynomial functions: (a) f ( x ) = 9 x 2 ? 6 x + 16 (b) f ( x ) = ? 2 3 x 3 ? 5 x + 3 x 2 + 10 (c) f ( x )...

Is \frac{x^4}{8} + \frac{5}{x} a rational function? If it is, write it as \frac{p(x)}{q(x)} where p(x) and q(x) are polynomials with no common factor.

Sketch the level curves, z = 1 & z = 4 for the function f(x, y) = x^{1 / 3} y^{2 / 3}, x greater than 0, y greater than 0.

sketch the curve. y = fraction {x}{x^2 - 16}

Find the following quotient \frac{3x^2-7x+1}{3x^2+5x-2} \div \frac{2x^2+3x+2}{3x^2+11x-4}

Sketch the curve of y= fraction {x}{x^2-4}

Analyze the graph of f(x)=\frac{2(x^{2}-9)}{x^{4}-4}

Consider the following. g(x) = (x^2 - 3x - 10)/(x^2 - 36). A) State the domain of the function. B) Identify all intercepts. C) Find any vertical and horizontal asymptotes.

What does the graph of: ='false' \frac {(2z + sin(z))}{z} look like

Consider the function f(x, y):= xy^3/x^4 + y^4. (a) Find the maximal domain D so that f mapping D to R is a function (i.e. find all points (x, y) at which f is defined). (b) At which points of D fr...

f(x) = fraction {x}{square root {x^2 + 3} - 2x } find the verticle asymptotes of f(x) Find the horizontal asymptotes of f(x), make sure with both direction of the x-axis.

Evaluate the integral: integral fraction {x^2 - 48}{x+7}dx

Sketch the graph of the following function. Indicate where the function is increasing or decreasing, where any relative extrema occur, where asymptotes occur, where the graph is concave up or conca...

Let f(x) = \frac{2x^2-18}{x^2 + x - 2} . Find the domain of the function. Find the vertical and horizontal asymptotes. Find the x-intercepts and y-intercepts.

Analyze and sketch a graph of the function. Find any intercepts, relative extremes, points of inflection, and asymptotes. y = x x 2 + 64

Analyze the function f(x)= (x^3-4x^2-31x+70)/(x^2-5x+6). Find the y-intercept, the x-intercept(s), the removable singularities, the vertical asymptotes and the horizontal asymptotes.

Let f(x) = \frac{2x^2 - 18}{x^2 + x - 2} . a) Find the domain of the function. b) Find the vertical and horizontal asymptotes of the graph of f(x) if they are any. c) Find the x-intercepts and y-i...

Give an example of a rational function f(x) that is continuous for all values of x except at x = \frac{+}{-5} , where it has non-removable discontinuities, and at x = 2, where it has a removable d...

Classify as a polynomial, a power function, or a rational function. y = frac{x}{(x + 1)^2}

1. Which equation matches the graph? \\
f(x)= sqrt (x2 + 4) \\
f(x)= sqrt (x2 - 3) \\
f(x)= sqrt (x + 3) \\
f(x)= sqrt (x - 2) \\
f(x)= sqrt (-2x +5)

Find a formula for a function f that satisfies the following conditions. lim_ {x to plus or minus infinity} f(x) = 0, lim_ {x to 0} f(x) = - infinity, f(7) = 0. lim_{x to 8-} f(x) = infinity, lim_...

Consider the functions: f(x)=3/x+1 and g(x)=1/x+2 A) Using interval notation, state the domain of f(x)and the domain of g(x). B) Write a formula for the difference function h(x)=f(x)-g(x). Write yo...

What is a rational equation?

Consider the function f(x) = \frac{x^2}{x^2-16} . a. Find the vertical and horizontal asymptotes. b. Find the interval where the function is increasing or decreasing. c. Find the local maximum v...

Consider the function f(x) = 1/x + 1. a) State the domain of the function f. b) State all limits associated with vertical or horizontal asymptotes for the graph of y = f(x). c) Draw and label the g...

Find a formula for a function that satisfies the following conditions \lim_{x\rightarrow \pm \infty} f(x) = 0 \\ \lim_{x\rightarrow 0} f(x) = -\infty \\ \lim_{x\rightarrow 0^-} f(x) = \infty \\ \...

Find and sketch the domain of the function f(x)= \sqrt{1-x^2}\sqrt{9-y^2}

1. Find all roots, vertical and horizontal asymptotes, intervals of increase/decrease, intervals of concavity, and local maximum and local minimum values of the following functions. Using this info...

Determine the set of points at which the function below is continuous. F(x, y) = (1 + x^2 + y^2)/(5 - x^2 - y^2).

Evaluate the integral: integral of (x^3 + x^2 + x - 1)/(x^2 + 2x + 2) dx.

Analyze the function: f(x) = sqrt[ (x^2 + x) / (x^2 - x) ]

Let f be the function that is given by f (x) = (ax + b) / (x^2 - c), such that the graph of f is symmetric with respect to the y-axis, the graph of f has a vertical asymptote at x = 2, and the gr...

Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of inflection and asymptotes. (If an answer does not exist, enter DNE.) y = \frac{4x}{x^{2} - 1}. Find the...

Find the limit: limit as x approaches -5 of (x^2 + 3x - 10)/(x + 5).

Consider the function A(x)=xsqrtx+9 . (a) Find the interval of increase. Find the interval of decrease. (b) Find the local minimum value. (c) Find the interval the function is concave up. (d) Use...

Analyze and sketch a graph of the function y = -x^2 - 4x - 7 x + 3 . Find any intercepts, relative extrema, points of inflection, and asymptotes.

For the function g(x, y, z) = e^{xyz} x + y + z, evaluate the following. (a) g(0, 0, 0) (b) g(1, 0, 0) (c) g(0, 1, 0) (d) g(z, x, y) (e) g(x + h, y + k, z + l)

Analyze and sketch a graph of the function: \displaystyle f(x)=\frac{x^3}{x^2-81}. Find any intercepts, relative extrema, points of inflection, and asymptotes.

Consider \displaystyle f(x)=\frac{x}{x-1}. a) Find all intercepts. b) Find all asymptotes. c) Find f^{-1}(x). d) Find the domain and range of f(x). e) Sketch a graph.

Find all roots, vertical and horizontal asymptotes, intervals of increase/decrease, intervals of concavity, and local maximum and local minimum values of the following functions. Using this informa...

Sketch the graph of the function f(x) = \frac{x-2}{x^2-5x+6} , showing all asymptotes, intercepts, extrema and points of inflection.

For f(x) = (x - 4)(x - 3)(x - 2)( x- 1) / (x - 4)(x - 2) find the domain, removable discontinuities, x and y intercepts, and asymptotes.

How to find holes in a rational function

Analyze and sketch a graph of the function f(x) = (x^2 + 64)/(x), then find any intercepts, relative extrema, points of inflection and asymptotes.

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