Graph each function. See Examples 6–8 and the Summary of Graphing Techniques box following Example 9. ƒ(x)=x²+2

For each function, find (a) ƒ(2) and (b) ƒ(-1).See Example 7. ƒ = {(-1,3),(4,7),(0,6),(2,2)}

Solve each problem. A graph of y=ƒ(x) is shown in the standard viewing window. Which is the only value of x that could possibly be the solution of the equation ƒ(x) =0? A. -15 B. 0 C. 5 D. 15

Find and interpret the average rate of change illustrated in each graph.

For each function, find (a) ƒ(2) and (b) ƒ(-1).See Example 7. ƒ = {(2,5),(3,9),(-1,11),(5,3)}

Graph each function.

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

Use a graphing calculator to solve each linear equation. 7x-2x+ 4-5=3x+1

Graph each function.

$\text{ƒ}\left(x\right)=-\mid x\mid$

Graph each function.

$\text{ƒ}\left(x\right)=-\text{√}x-2$

Given functions f and g, find (a)$(\text{ƒ}\circ g)\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=-6x+9,g\left(x\right)=5x+7$

Given functions f and g, (b)$(g\circ \text{ƒ})\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=-6x+9,g\left(x\right)=5x+7$

Given functions f and g, find (a)$(\text{ƒ}\circ g)\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=8x+12,g\left(x\right)=3x-1$

Given functions f and g, find (b)$(g\circ \text{ƒ})\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=8x+12,g\left(x\right)=3x-1$

Given functions f and g, find (a)$(\text{ƒ}\circ g)\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\text{√}x,g\left(x\right)=x+3$

Given functions f and g, find (b)$(g\circ \text{ƒ})\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\text{√}x,g\left(x\right)=x+3$

Consider the following nonlinear system. Work Exercises 75 –80 in order.

$y=\mid x-1\mid$

$y=x^2-4$

How is the graph of y = x^2 - 4 obtained by transforming the graph of $y=x^2$?

If three distinct points A, B, and C in a plane are such that the slopes of nonvertical line segments AB, AC, and BC are equal, then A, B, and C are collinear. Otherwise, they are not. Use this fact to determine whether the three points given are collinear. (-1, -3), (-5, 12), (1, -11)

Given functions f and g, find (a)$(\text{ƒ}\circ g)\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=x^3,g\left(x\right)=x^2+3x-1$

Given functions f and g, (b)$(g\circ \text{ƒ})\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=x^3,g\left(x\right)=x^2+3x-1$

An equation that defines y as a function of x is given. (b) Find ƒ(3). x-4y=8

Given functions f and g, find (a)$(\text{ƒ}\circ g)\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=x+2,g\left(x\right)=x^4+x^2-4$

Given functions f and g, find (b)$(g\circ \text{ƒ})\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=x+2,g\left(x\right)=x^4+x^2-4$

An equation that defines y as a function of x is given. (b) Find ƒ(3). y+2x²=3-x

Given functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\text{√}(x-1),g\left(x\right)=3x$

Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\text{√}(x-1),g\left(x\right)=3x$

Graph each function. See Examples 6–8 and the Summary of Graphing Techniques box following Example 9. ƒ(x)=-3(x-2)²+1