# Understanding Functions Flashcards

## Flashcard Content Overview

There are many characteristics of a function, and this flashcard set will cover a lot of them. Using this flashcard set will aid in retention of facts about functions and in just understanding functions in general. It will cover such concepts as domain and range of a function, adding, subtracting, multiplying and dividing functions, composition of functions, graphs of functions, inverse functions, and function transformations. There's also a couple flashcards that allow you to practice applications of these concepts in a real-world context.

The possible values of *x* that we can put into the function.

*f*(

*x*) = √(

*x*+ 2), and

*g*(

*x*) =

*x*- 3, find the domain of

*f*(

*x*) /

*g*(

*x*).

Domain = [-2, 3) ∪ (3, ∞)

A function that takes more than one expression to define for different intervals of *x*.

*f*(2)

-2

An equation or rule that you plug an input into and get an output out of.

is

A set of ordered pairs relating the first coordinates to the second coordinates by some rule.

*f*(

*x*) = 7

*x*- 2, find

*f*(3).

19

*f*(

*x*) =

*x*2 + 10

*x*+ 1000, and the average product price is

*g*(

*x*) = 4

*x*+ 50. Find the revenue model.

*r*(*x*) = 4*x*3 + 90*x*2 + 4500*x* + 50000

A function that tells how much money a company makes.

*f* (*x*) = 3*x*4 - 2*x*3 + *x* - 4

*g*(*x*) = 7*x*2 + 2*x* + 1

Find *f* (*x*) - *g*(*x*).

*f* (*x*) - *g*(*x*) = 3*x*4 - 2*x*3 - 7*x*2 - *x* - 5

*f* (*x*) = 5*x*2 + 4*x*

*g*(*x*) = 3*x*

Find *f* (*x*) / *g*(*x*).

*f* (*x*) / *g*(*x*) = (5*x* + 4) / 3, *x* ≠ 0

*f* (*x*) = 2*x*2 + 5*x* + 3

*g*(*x*) = *x*2 - 3*x* - 4

Find *f* (*x*) / *g*(*x*).

*f* (*x*) / *g*(*x*) = (2*x* + 3) / (*x* - 4), *x* ≠ -1, 4

Plugging a function into another function.

*f* (*x*) = *x*2 - 1

*g*(*x*) = *x* + 1

Find *f* (*g*(*x*)).

*x*2 + 2*x*

*f*(

*g*(

*x*)) = √(

*x*+ 4), what is

*f*(

*x*) and

*g*(

*x*)?

*f* (*x*) = √(*x*) and *g*(*x*) = *x* + 4

*f*(

*x*) =

*x*3 - 2

*x*and

*g*(

*x*) = |

*x*|, find

*f*(

*g*(-2)).

4

A function that is the opposite of, or undoes, another function.

*f*(

*x*) and

*g*(

*x*) are inverse functions

If *f* (*x*) and *g*(*x*) are inverse functions, then *f* (*g*(*x*)) = *g*(*f* (*x*)) = *x*.

If a horizontal line passes through the graph of a function more than once, then the function does not have an inverse.

1. Replace *f* (*x*) with *y*.

2. Interchange *x* and *y*.

3. Solve for *y*

4. Replace *y* with *f* -1 (*x*).

*g*(

*x*) in terms of

*f*(

*x*)

*g*(*x*) = *f* (*x* + 5)

*g*(

*x*) in terms of

*f*(

*x*)

*g*(*x*) = *f* (*x*) - 4

Sliding a graph along a straight line

Reflecting a graph over a line

*y*=

*x*

Reflected over *y* = *x*

*f* (*x*) = *x*2 + 3

*g*(*x*) = √(*x* + 3)

Find the domain of *f* (*g*(*x*))

Domain = all numbers greater than or equal to -3.

(When you find the domain of f(g(x)), you have to take into account the domain of the original function g(x) even though it gets squared in forming the new function.)

*f*(

*x*)

All real numbers

Possible output values of the function

*f*(

*x*)

Range = all real numbers greater than or equal to 1

*f*(

*x*) = 1 /

*x*

0

*f*(

*x*) = 4 / (

*x*2 +

*x*- 42)

Domain = all real numbers except -7 and 6

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Math 103: Precalculus14 chapters | 121 lessons | 10 flashcard sets

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- Go to Functions

- Understanding Functions Flashcards
- Understanding Inequalities Flashcards
- Foundations of Linear Equations Flashcards
- Graphing Rational Equations Flashcards
- Factoring & Graphing Quadratic Equations Flashcards
- Understanding Exponents & Polynomials Flashcards
- Piecewise & Composite Functions Flashcards
- Overview of Geometry & Trigonometry Flashcards
- Basic Trigonometry Flashcards
- Math 103: Precalculus Formulas & Properties
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