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?

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].