Chapter 0.2, Problem 49E

a.

To determine

To plot: The graph of the function $f\left(x\right)=-\left|3-x\right|+2$ .

Explanation of Solution

Given information:

The given function is $f\left(x\right)=-\left|3-x\right|+2$

Plot the graph:

The function is $f\left(x\right)=-\left|3-x\right|+2$ where center at the point $\left(3,2\right)$ ,the graph of the function is given below.

  

b.

To determine

To find: The range of the function $f\left(x\right)=-\left|3-x\right|+2$ .

Answer to Problem 49E

Then range will be $\left\{y\in R,y\le 2\right\}$ .

Explanation of Solution

Given information:

The given function is $f\left(x\right)=-\left|3-x\right|+2$

Concept used:

The range of the function is the set of all output values.

Calculations:

Here $f\left(x\right)=-\left|3-x\right|+2$ .

Range is the set of all output value or the $y$ values. Then range will be $\left\{y\in R,y\le 2\right\}$

c.

To determine

To find: The domain of the function $f\left(x\right)=-\left|3-x\right|+2$ .

Answer to Problem 49E

domain will be set of all real numbers. $\left\{x\in R\right\}$

Explanation of Solution

Given information:

The given function is $f\left(x\right)=-\left|3-x\right|+2$

Concept used:

The domain of the function is the set of all input values or independent value.

Calculations:

Here $f\left(x\right)=-\left|3-x\right|+2$ .

Domain is the set of all input value or the $x$ values. So here domain will be set of all real numbers. $\left\{x\in R\right\}$ .