https://file.aiquickdraw.com/mathbot/file/1726104182969heitlnw6.jpg

Let's break down the problem step by step based on what is visible from the image you provided:

### Part c: Evaluate the function for \( h = 7 \)
The function you're given seems to be of the form \( M(h) = 13h + 200 \).

For \( h = 7 \), the equation is:
\[
M(7) = 13(7) + 200 = 91 + 200 = 291
\]
So, \( M(7) = 291 \).

### Part d: Make a table and graph for the function
To create a table for this function \( M(h) = 13h + 200 \), you can calculate the function for different values of \( h \). Here's an example:

| \( h \) | \( M(h) = 13h + 200 \) |
|--------|-------------------------|
| -4     | \( 13(-4) + 200 = 148 \) |
| -2     | \( 13(-2) + 200 = 174 \) |
| 0      | \( 13(0) + 200 = 200 \)  |
| 2      | \( 13(2) + 200 = 226 \)  |
| 4      | \( 13(4) + 200 = 252 \)  |
| 7      | \( 13(7) + 200 = 291 \)  |

Now, you can graph these points on the coordinate plane for a visual representation.

### Part e: Determine domain and range
The function \( M(h) = 13h + 200 \) is a linear function, so it has the following characteristics:
- **Domain**: Since this is a linear function, \( h \) can be any real number, so the domain is \( (-\infty, \infty) \).
- **Range**: As \( h \) increases or decreases without bound, \( M(h) \) also increases or decreases without bound. Therefore, the range is also \( (-\infty, \infty) \).

### Graph and Impact of the Domain/Range
Since the function is linear, the graph will be a straight line. Changing the domain (e.g., restricting \( h \) to certain values) will limit the extent of the graph that is displayed, but the overall shape of the function does not change.

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Would you like further details or have any questions about the problem so far? Here are five related questions to deepen your understanding:

1. How do you determine the slope of a linear function?
2. What happens to the graph if the constant term changes (e.g., if the 200 changes)?
3. How would the domain and range change if the function was a quadratic instead of linear?
4. How does the table of values help in sketching the graph?
5. What is the significance of the \( y \)-intercept in the graph of the function?

**Tip**: Always remember, in a linear function, the slope determines the steepness of the line, and the constant term affects the vertical shift (where the graph intersects the y-axis).

Evaluate the function for h = 7, make a table and graph for the function, and determine the appropriate domain and range.

Learn how to evaluate the linear function M(h) = 13h + 200 for h = 7, create a table of values, graph the function, and determine the domain and range. This problem is suitable for students in Grades 7-9.

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