Chapter 3, Problem 15CR

For the graph of the function $f$,

a. Find the domain and the range of $f$.

b. Find the intercepts.

c. Is the graph of $f$ symmetric with respect to the $x\text{-axis}$, the $y\text{-axis}$, or the origin?

d. Find $f\left(2\right)$.

e. For what value(s) of $x$ is $f\left(x\right)=3$?

f. Solve $f\left(x\right)<0$.

g. Graph $y=f\left(x\right)+2$.

h. Graph $y=f(-x)$.

i. Graph $y=2f\left(x\right)$.

j. Is $f$ even, odd, or neither?

k. Find the interval(s) on which $f$ is increasing.

To determine

a. The domain and range of $f$.

b. The intercepts.

c. Symmetry

d. $f\left(2\right)$

e. When $f(x)=3$, what is $x$?

f. Solve $f(x)<0$

g. Graph $y=f(x)+2$

h. Graph

i. Graph

j. Is $f$ even, odd or neither.

k. Where is $f$ increasing?

Answer to Problem 15CR

Solution:

a. The domain is $(-4,4)$ and the range is $(-1,3)$.

b. The $x\text{-intercept}$ is at $(-1,0)$ and $(1,0)$. The $y\text{-intercept}$ is at $(0,-1)$.

c. The graph is symmetric about the $y\text{-axis}$.

d. $f(2)=1$

e. When $f(x)=3$, we have $x=4$.

f. When $f(x)<0$, we have $x\in (-1,1)$.

g. Graph $y=f(x)+2$

h. Graph $y=f(-x)$

i. Graph $y=2f(x)$

j. Is $f$ even, odd or neither.

k. $f$ is increasing in the interval $[0,4]$.

Explanation of Solution

Given:

Formula used:

Domain is the set of all $x$ (input) values.

Range is the set of all $y$ (output) values.

Calculation:

l. The domain is $(-4,4)$ and the range is $(-1,3)$.

m. The $x\text{-intercept}$ is at $(-1,0)$ and $(1,0)$. The $y\text{-intercept}$ is at $(0,-1)$.

n. The graph is symmetric about the $y\text{ axis}$.

o. $f(2)=1$

p. When $f(x)=3$, we have $x=4$.

q. When $f(x)<0$, we have $x\in (-1,1)$.

r. Graph $y=f(x)+2$

s. Graph $y=f(-x)$

t. Graph $y=2f(x)$

u. Is $f$ even, odd or neither.

v. $f$ is increasing in the interval $[0,4]$.