Chapter 3.2, Problem 22PPS

To determine

The zero of the function and also the domain and range.

Answer to Problem 22PPS

$40

Domain: $(-\infty ,40)\cup (40,-\infty )$

Range: $-\infty \le y\le \infty .$

Explanation of Solution

Given:

Function: $y=160-4x$

Where $m$ is the amount of money that remains after spending $4 on meals.

Calculation:

Sean budgets $160 for a month to cover the school lunch expenses and additional dining expenses.

To find the amount of money, solve the given function $y=160-4x.$

Consider $y=0,$

  $\begin{array}{c}y=160-4x\\ 0=160-4x\\ -160=-4x\text{ [Subtract 160 on both sides]}\\ 160=4x\\ x=\frac{160}{4}\text{ [Divide by 4 on both sides]}\\ x=40\end{array}$

Domain of the function is $(-\infty ,40)\cup (40,-\infty )$

To find the range of the given function,

To graph the function, make a table.

$x$	$y(x)=160-4x$	$y(x)$	$(x,y(x))$
0	$y(0)=160-4(0)$	160	$(0,160)$
10	$y(10)=160-4(10)$	120	$(10,120)$
20	$y(20)=160-4(20)$	80	$(20,80)$
30	$y(30)=160-4(30)$	40	$(30,40)$
40	$y(40)=160-4(40)$	0	$(40,0)$
50	$y(50)=160-4(50)$	-40	$(50,-40)$

Graph:

  

Interpretation:

From the graph, it is clear that,

The range of the function is $-\infty \le y\le \infty .$