Chapter 2.2, Problem 10AYU

Use the given graph the function $f$ to answer parts (a)-(n).

(a) Find $f\left(0\right)$ and $f\left(6\right)$.

(b) Find $f\left(2\right)$ and $f\left(-2\right)$.

(c) Is $f\left(3\right)$ positive or negative?

(d) Is $f\left(-1\right)$ positive or negative?

(e) For what values of $x$ is $f\left(x\right)\text{ = 0}$?

(f) For what values of $x$ is $f\left(x\right)<\text{ 0}$?

(g) What is the domain of $f$?

(h) What is the range of $f$?

(i) What are the $x\text{-intercepts}$?

(j) What is the $y\text{-intercept}$?

(k) How often does the line $y=-1$ intersect the graph?

(l) How often does the line $x=1$ intersect the graph?

(m) For what values of $x$ does $f\left(x\right)=3$?

(n) For what values of $f\left(x\right)=-2$?

To determine

To find:

a. $f\left(0\right)$ and $f\left(6\right)$.

Answer to Problem 10AYU

Solution:

a. $f\left(0\right)= 0, f\left(6\right)=0$;

Explanation of Solution

Given:

The following graph

Calculation:

a. $f\left(0\right)= 3, f\left(-6\right)=-3$;

To determine

To find:

b. $f\left(2\right)$ and $f(-2)$.

Answer to Problem 10AYU

Solution:

b. $f\left(2\right)=-2,f(-2)=1$;

Explanation of Solution

Given:

The following graph

Calculation:

b. $f\left(6\right)=0,f(11)=1$;

To determine

To find:

c. $f(3)$ positive or negative.

Answer to Problem 10AYU

Solution:

c. $f\left(3\right)$ is negative as the curve is below the $x\text{-axis}$;

Explanation of Solution

Given:

The following graph

Calculation:

c. $f\left(3\right)$ is positive as the curve is above the $x\text{-axis}$;

To determine

To find:

d. $f\left(-1\right)$ positive or negative.

Answer to Problem 10AYU

Solution:

d. $f\left(-4\right)$ is positive as the curve is above the $x\text{-axis}$;

Explanation of Solution

Given:

The following graph

Calculation:

d. $f\left(-1\right)$ is negative as the curve is below the $x\text{-axis}$;

To determine

To find:

e. Value of $x$ for which $f\left(x\right)=0$.

Answer to Problem 10AYU

Solution:

e. $f\left(x\right)=0$ when $x=0,4,6$;

Explanation of Solution

Given:

The following graph

Calculation:

e. $f\left(x\right)=0$ when $x=-3,6,10$;

To determine

To find:

f. Value of $x$ for which $f\left(x\right)<0$.

Answer to Problem 10AYU

Solution:

f. $f\left(x\right)>0$ when $-4< x < 0;4< x<6$;

Explanation of Solution

Given:

The following graph

Calculation:

f. $f\left(x\right)>0$ when $-3< x < 6;10< x<11$;

To determine

To find:

g. Domain of $f$.

Answer to Problem 10AYU

Solution:

g. Domain of $f=\left\{x|-4\le x\le 6\right\}$;

Explanation of Solution

Given:

The following graph

Calculation:

g. Domain of $f=\left\{x|-6\le x\le 11\right\}$;

To determine

To find:

h. Range of $f$

Answer to Problem 10AYU

Solution:

h. Range of $f=\left\{x|-2\le y\le 3\right\}$;

Explanation of Solution

Given:

The following graph

Calculation:

h. Range of $f=\left\{x|-3\le y\le 4\right\}$;

To determine

To find:

i. Intercepts of $x$.

Answer to Problem 10AYU

Solution:

i. Intercepts of $x=0,4,6$;

Explanation of Solution

Given:

The following graph

Calculation:

i. Intercepts of $x=-3,6,10$;

To determine

To find:

j. Intercepts of $y$.

Answer to Problem 10AYU

Solution:

j. Intercept of $y=0$;

Explanation of Solution

Given:

The following graph

Calculation:

j. Intercept of $y=3$;

To determine

To find:

k. Number of times the line $y=-1$ intersect the graph.

Answer to Problem 10AYU

Solution:

k. The line $y=-1$ crosses the curve three times;

Explanation of Solution

Given:

The following graph

Calculation:

k. The line $y=\frac{1}{2}$ crosses the curve three times;

To determine

To find:

l. Number of times the line $x=1$ intersect the graph.

Answer to Problem 10AYU

Solution:

l. The line $x=1$ crosses the curve only once;

Explanation of Solution

Given:

The following graph

Calculation:

l. The line $x=5$ crosses the curve only once;

To determine

To find:

m. The values of $x$ for which $f\left(x\right)=3$.

Answer to Problem 10AYU

Solution:

m. When $x=5,f\left(x\right)=3,\left(5,3\right)$;

Explanation of Solution

Given:

The following graph

Calculation:

m. When $x=0,f\left(x\right)=3,\left(0,3\right)$;

To determine

To find:

n. The values of $x$ for which $f\left(x\right)=-2$.

Answer to Problem 10AYU

Solution:

n. When $x=2,f\left(x\right) =-2,\left(2,-2\right)$;

Explanation of Solution

Given:

The following graph

Calculation:

n. When $x=8,f\left(x\right) =-2,\left(8,-2\right)$;