https://file.aiquickdraw.com/mathbot/file/1727038249937catqilak.jpg

Let's go through the problems one by one based on the image provided.

### (a) Finding the values of \( h(x) \) for specific inputs:
From the graph, you can read the function values for the given \( x \)-values.

- \( h(-2) = -1 \)
- \( h(0) = -3 \)
- \( h(2) = 2 \)
- \( h(3) = 1 \)

### (b) Domain and Range of \( h \):

- **Domain:** The domain consists of all \( x \)-values for which the function is defined. From the graph, the function is defined from \( x = -5 \) to \( x = 6 \). So, the domain is:
  \[
  [-5, 6]
  \]
  
- **Range:** The range consists of all \( y \)-values that the function takes. From the graph, the minimum \( y \)-value is \( -3 \), and the maximum \( y \)-value is \( 4 \). So, the range is:
  \[
  [-3, 4]
  \]

### (c) Finding values of \( x \) for which \( h(x) = 2 \):

From the graph, you can see that \( h(x) = 2 \) occurs at two points:

- \( x = 2 \)
- \( x = 4 \)

Thus, the values of \( x \) are:
\[
x = 2, 4
\]

### (d) Finding values of \( x \) for which \( h(x) \leq 2 \):

From the graph, \( h(x) \leq 2 \) occurs in the intervals:
- \( x \in [-3, 2] \) and at \( x = 4 \)

So, the correct answer is:
\[
[-3, 2] \text{ and } 4
\]

### (e) Finding the net change in \( h \) between \( x = -3 \) and \( x = 3 \):

- \( h(-3) = 0 \)
- \( h(3) = 1 \)

The net change is:
\[
h(3) - h(-3) = 1 - 0 = 1
\]

---

Do you have any questions about these answers or want more details on any step? Here are 5 related questions to expand on these topics:

1. How would you find the values of \( x \) for which \( h(x) = -1 \)?
2. Can you explain how to determine if a function is increasing or decreasing on a specific interval from a graph?
3. What would the graph look like if the range was extended to \( [-5, 5] \)?
4. How do you determine the derivative of a function given its graph?
5. Can you find the average rate of change of \( h(x) \) between \( x = -5 \) and \( x = 6 \)?

**Tip:** When analyzing a function's graph, always check where the function crosses key values like \( y = 0 \), since these intersections can provide critical points for solving equations.

The graph of a function h is given. Find values of h at specific points, domain and range, and solve for certain conditions.

Learn how to analyze a function graph to find the values of h(x) at given points, domain, range, and solve for specific conditions such as h(x) = 2. This problem focuses on interpreting graphs, domain, range, and net change.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation