Chapter 1, Problem 106RE

a.

To determine

To identify : the parent function.

Answer to Problem 106RE

The parent function is $f\left(x\right)=\frac{1}{x}$.

Explanation of Solution

Given information :

The function is $h\left(x\right)=\frac{5}{x+2}-4$.

form the function provided in the question it can be observed that the function is transformed by the parent function of $f\left(x\right)=\frac{1}{x}$.

b.

To determine

To describe : the sequence of transformations $f$ to $h$.

Answer to Problem 106RE

shift the graph 2 unit left then stretch the graph vertically by a factor of $5$ then shift it $4$ unit downwards.

Explanation of Solution

Given information :

The function is $h\left(x\right)=\frac{5}{x+2}-4$.

since parent function is $f\left(x\right)=\frac{1}{x}$ ,to transform the graph form $f$ to $h$ , first shift the graph 2 unit left then stretch the graph vertically by a factor of $5$ then shift it $4$ unit downwards.

c.

To determine

To draw : the graph of function h.

Explanation of Solution

Given information :

The function is $h\left(x\right)=\frac{5}{x+2}-4$.

graph : first, to graph the parent function use the point plotting,

x	1	-2	-3	-4
y	1	$-\frac{1}{2}$	$-\frac{1}{3}$	$-\frac{1}{4}$

Now, shift the graph 2 unit left then stretch the graph vertically by a factor of $5$ then shift it $4$ unit downwards.

Thus, the graph can be obtained as:

  

Interpretation: from the above graph it can be observed thatto graph $h\left(x\right)=\frac{5}{x+2}-4$ ,shift the graph 2 unit left then stretch the graph vertically by a factor of $5$ then shift it $4$ unit downwards.

d.

To determine

To find : the function h in the terms of function of f.

Answer to Problem 106RE

the function h in the terms of function of f is $h\left(x\right)=5f\left(x+2\right)-4$.

Explanation of Solution

Given information :

The function is $h\left(x\right)=\frac{5}{x+2}-4$.

Calculation : since $f\left(x\right)=\frac{1}{x}$ , to write the function h in the terms of function of f substitute $f\left(x\right)=\frac{1}{x}$ in the function h.

  $\begin{array}{l}h\left(x\right)=\frac{5}{x+2}-4\\ h\left(x\right)=5f\left(x+2\right)-4\text{ [substitute }f\left(x\right)=\frac{1}{x}]\end{array}$

Hence, the function h in the terms of function of fis $h\left(x\right)=5f\left(x+2\right)-4$.