High School

We appreciate your visit to Taylor makes 13 per hour at the grocery store She always works between 10 15 hours per week to leave time for her homework and. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Taylor makes \$13 per hour at the grocery store. She always works between 10-15 hours per week to leave time for her homework and band practice. Her gross wages can be modeled as [tex]w(h) = 13h[/tex], where [tex]h[/tex] is the number of hours worked per week.

a. How much will her gross wages be if she works 12 hours this week?

[tex]\$156[/tex]

b. What is the domain of this function?

c. What is the range of this function?

Answer :

Sure, let's break this down step-by-step:

### Given Information:
- Taylor makes \[tex]$13 per hour.

### Part (a)
We need to find out how much her gross wages will be if she works 12 hours in a week.

Calculation:
Gross wages, \( w(h) = 13h \)

If \( h = 12 \):
\[ w(12) = 13 \times 12 = 156 \]

So, her gross wages will be \$[/tex]156 if she works 12 hours this week.

### Part (b)
We need to determine the domain of the function [tex]\( w(h) = 13h \)[/tex].

Explanation:
The domain represents all possible values for [tex]\( h \)[/tex] (the number of hours worked per week).

Taylor works between 10 and 15 hours per week. Therefore,
[tex]\[ \text{Domain} = \{ h \mid 10 \leq h \leq 15 \} \][/tex]
Or in interval notation:
[tex]\[ \text{Domain} = [10, 15] \][/tex]

### Part (c)
We need to find the range of the function [tex]\( w(h) = 13h \)[/tex].

Explanation:
The range represents all possible values of her gross wages based on the number of hours worked per week.

Given the range of hours (10 to 15 hours):
- The minimum possible gross wage (when [tex]\( h = 10 \)[/tex]) is [tex]\( 13 \times 10 = 130 \)[/tex]
- The maximum possible gross wage (when [tex]\( h = 15 \)[/tex]) is [tex]\( 13 \times 15 = 195 \)[/tex]

Therefore, the range of gross wages is:
[tex]\[ \text{Range} = \{ w(h) \mid 130 \leq w(h) \leq 195 \} \][/tex]
Or in interval notation:
[tex]\[ \text{Range} = [130, 195] \][/tex]

### Summary of Answers:
(a) If Taylor works 12 hours this week, her gross wages will be \$156.

(b) The domain of the function is [tex]\([10, 15]\)[/tex].

(c) The range of the function is [tex]\([130, 195]\)[/tex].

Thanks for taking the time to read Taylor makes 13 per hour at the grocery store She always works between 10 15 hours per week to leave time for her homework and. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada