Chapter 3, Problem 45SGR

To determine

Describe the graph of the function change if base salary increases to $450.

Answer to Problem 45SGR

If her base salary increases to $450 then the graph of the function g(x) will shift 50 units upward to the graph of function p(x).

Explanation of Solution

Given information:

Weekly pay is described by the function $p\left(x\right)=0.25x+400,$ where x is the number of weeks.

Solution: If we compare given function $p\left(x\right)=0.25x+400,$ by slope-intercept form $y=mx+b$ , we can see that b=400.

Therefore, according to given function base salary is $400.

If, the initial base salary is increase to $450, that means we are increasing $50 in base salary.

So, the new function would be $g(x)=p\left(x\right)+50$ , where $g(x)$ is the new total weekly pay.

According to rule of transformation $g(x)=p(x)+k,\text{ the graph of g(}x\text{) shifts upward }k\text{ units}\text{.}$

Substitute $p\left(x\right)=0.25x+400,$ in $g(x)=p\left(x\right)+50$ , we get

  $\begin{array}{l}g(x)=0.25x+400+50\\ \Rightarrow g(x)=0.25x+450\end{array}$

Therefore, by the rule of transformation g(x) is shifted upward 50 units.