3. Functions

Express the given function h as a composition of two functions f and g so that h(x) = (f ○ g)(x). h(x) = (x² + 2x - 1)⁴

Use the graphs of f and g to evaluate each composite function.

(fog) (-1)

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y² – 10x – 6y – 30 = 0

Find fg and determine the domain for each function. f(x) = 3 − x², g(x) = x² + 2x − 15

Describe the graph of each equation as a circle, a point, or nonexistent. If it is a circle, give the center and radius. If it is a point, give the coordinates. x²+y²-2x+12y-12=0

Fill in the blank(s) to correctly complete each sentence. The domain of the relation { (3,5), (4, 9), (10, 13) } is _____.

Use the graphs of f and g to solve Exercises 83–90.

Graph f-g.

Find f−g and determine the domain for each function. f(x) = 2x² − x − 3, g (x) = x + 1

To answer each question, refer to the following basic graphs. Which one is the graph of ƒ(x)=∛x? Is there any open interval over which the function is decreasing?

Express the given function h as a composition of two functions ƒ and g so that h(x) = (fog) (x).

h(x) = 1/(2x-3)

Graph each function.

$\text{ƒ}\left(x\right)=\mid x\mid -3$

Determine whether each relation defines y as a function of x. Give the domain and range. See Example 5. y=-6x+4

In Exercises 77–92, use the graph to determine a. the function's domain; b. the function's range; and e. the missing function values, indicated by question marks, below each graph.

Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. g(k)

Fill in the blank to correctly complete each sentence. The point (-1, 3) lies in quadrant ________ in the rectangular coordinate system.