Let function f(x) be defined by f(x) = 7 - sqrt{x^2 + 2x + 5}. (a) Sketch the graph of f(x) by...

The terms under radical symbols with the same index can be combined through multiplication, then simplified. Learn how to multiply and simplify radical expressions by using the product rule, and review the examples.

According to the fundamental theorem of arithmetic, all positive numbers except 1 can be expressed as a product of prime numbers. Explore this concept by learning more about arithmetic and prime numbers, and gain understanding by considering examples.

Know what sine and cosine waves are and how to graph their respective waves. Read more about the calculation of its period and amplitude through examples here.

Continuous functions are functions that have their conditions satisfied between multiple points, appearing as an uninterrupted line when graphed. See examples of how this is represented in the intermediate value theorem and the extreme value theorem.

The steps of multiplying or dividing rational polynomial expressions are to factor, flip (when dividing), slash or cancel, and multiply. Put these steps for multiplying and dividing rational expressions into action and master the concept by solving a series of example problems.

Learn about adding and subtracting rational expressions. Explore how to add and subtract rational expressions. See examples of operations with rational expressions.

Learn to define what a function means in math. Discover variables and other terms that explain math functions. Learn how to graph functions and see examples.

Exponential and logarithmic functions are the inverse of one another, the variable being in the exponent in the former and serving as the argument in the latter. Discover the definitions and behavior of these related functions.

What is a reciprocal function? View a reciprocal function graph and its traits, learn how to graph reciprocal functions, and see reciprocal function examples.

Learn about parabolas. Understand what a parabola is, learn how to find the focus of a parabola, examine the equation of parabolas, and see examples of parabolas.

What is a cubic function? See examples of cubic functions and learn how to graph cubic functions. Learn the equation and properties of a standard cubic function.

Learn how to graph a cube root function and a square root function. See what does a cube root function like and read about square root function transformations.

Absolute value definition. Learn the absolute value function equation, the domain of absolute value function, and see some absolute value function examples.

A trigonometric equation can be solved graphically by providing a visual demonstration of the mathematical answers. Learn how to find the answers graphically and understand what to watch out for when solving trigonometric equations.

What is an imaginary number? Learn about imaginary numbers, negative imaginary numbers, and imaginary number exponents. Also see imaginary number problems.

Learn the definition of a linear equation, along with the standard form and slope-intercept form of a linear equation. Also, know how to graph the standard form and the slope-intercept form of linear equations.