Chapter 1, Problem 102RE

a.

To determine

To identify : the parent function.

Answer to Problem 102RE

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

Explanation of Solution

Given information :

The function is $h\left(x\right)=\sqrt{x-1}+4$.

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

b.

To determine

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

Answer to Problem 102RE

shift the graph of parent function $f\left(x\right)=\sqrt{x}$ one unit right and then shift four unit upwards.

Explanation of Solution

Given information :

The function is $h\left(x\right)=\sqrt{x-1}+4$.

since parent function is $f\left(x\right)=\sqrt{x}$ ,to transform the graph form $f$ to $h$ , first shift the graph of parent function $f\left(x\right)=\sqrt{x}$ one unit right and then shift four unit upwards.

c.

To determine

To draw : the graph of function h.

Explanation of Solution

Given information :

The function is $h\left(x\right)=\sqrt{x-1}+4$.

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

x	1	4	9	16
y	1	2	3	4

Now ,shift the graph of parent function $f\left(x\right)=\sqrt{x}$ one unit right and then shift four unit upwards,

Thus, the graph can be obtained as:

  

Interpretation: from the above graph it can be observed thatto graph $h\left(x\right)=\sqrt{x-1}+4$ ,shift the graph of parent function $f\left(x\right)=\sqrt{x}$ one unit right and then shift four unit upwards.

d.

To determine

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

Answer to Problem 102RE

the function h in the terms of function of f is $h\left(x\right)=f\left(x-1\right)\text{+4}$.

Explanation of Solution

Given information :

The function is $h\left(x\right)=\sqrt{x-1}+4$.

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

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

Hence, the function h in the terms of function of fis $h\left(x\right)=f\left(x-1\right)\text{+4}$.