Chapter 0.2, Problem 50E

a.

To determine

To plot: The graph of the function $f\left(x\right)=2\left|x+4\right|+3$ .

Explanation of Solution

Given information:

The given function is $f\left(x\right)=2\left|x+4\right|+3.$

Plot the graph:

The function is $f\left(x\right)=2\left|x+4\right|+3$ where center at the point $\left(-4,3\right)$ ,the graph of the function is given below.

  

b.

To determine

To find: The range of the function $f\left(x\right)=2\left|x+4\right|+3$ .

Answer to Problem 50E

Then range will be $\left\{y\in R,y\ge 3\right\}$ .

Explanation of Solution

Given information:

The given function is $f\left(x\right)=2\left|x+4\right|+3$

Concept used:

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

Calculations:

Here $f\left(x\right)=2\left|x+4\right|+3$ .

Range is the set of all output value or the $y$ values. Then range will be $\left\{y\in R,y\ge 3\right\}$

c.

To determine

To find: The domain of the function $f\left(x\right)=2\left|x+4\right|+3$ .

Answer to Problem 50E

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

Explanation of Solution

Given information:

The given function is $f\left(x\right)=2\left|x+4\right|+3$

Concept used:

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

Calculations:

Here $f\left(x\right)=2\left|x+4\right|+3$ .

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