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Use the graph to determine a. the​ function's domain; b. the​ function's range; c. the​ x-intercepts, if​ any; d. the​ y-intercept, if​ any; and e. the missing function​ values, indicated by question​ marks, below.
f left parenthesis negative 2 right parenthesisf(−2)equals=​?   f left parenthesis 2 right parenthesisf(2)equals=​?

Let's analyze the provided graph and determine the requested information:

### a. Domain of the function
The domain of a function is the set of all possible \(x\)-values for which the function is defined. In this case, the curve extends from the left side of the graph at \(x = -5\) to the right side at \(x = 5\), so the domain is:

\[
\text{Domain} = [-5, 5]
\]

### b. Range of the function
The range is the set of all possible \(y\)-values that the function attains. The highest point on the graph occurs just below \(y = 3\), and the lowest point occurs at \(y = -5\). Therefore, the range is:

\[
\text{Range} = [-5, 3)
\]

(Note: The parenthesis for 3 indicates that the graph does not reach \(y = 3\), only very close to it.)

### c. \(x\)-intercepts
The \(x\)-intercepts are the points where the graph crosses the \(x\)-axis. From the graph, we can see that the curve crosses the \(x\)-axis at two points: \(x = -4\) and \(x = 2\). Thus, the \(x\)-intercepts are:

\[
x\text{-intercepts} = (-4, 0) \quad \text{and} \quad (2, 0)
\]

### d. \(y\)-intercept
The \(y\)-intercept is the point where the graph crosses the \(y\)-axis. The graph crosses the \(y\)-axis at \(y = -3\), so the \(y\)-intercept is:

\[
y\text{-intercept} = (0, -3)
\]

### e. Missing function values

- \( f(-2) \): To find \(f(-2)\), we look at the point on the graph where \(x = -2\). From the graph, it seems the corresponding \(y\)-value is around 2. Thus,

  \[
  f(-2) = 2
  \]

- \( f(2) \): Since \(x = 2\) is an \(x\)-intercept, the function value at \(x = 2\) is zero:

  \[
  f(2) = 0
  \]

### Summary of Results:
- **Domain**: \([-5, 5]\)
- **Range**: \([-5, 3)\)
- **\(x\)-intercepts**: \((-4, 0)\) and \((2, 0)\)
- **\(y\)-intercept**: \((0, -3)\)
- \( f(-2) = 2 \)
- \( f(2) = 0 \)

Would you like to go into more detail on any part? Here are some related questions:

1. How can the function's symmetry be described based on the graph?
2. What type of function might this be based on its shape (e.g., polynomial, quadratic)?
3. How could the graph be transformed (shifted or scaled) to match a different function?
4. What are the possible real-world applications of interpreting such functions?
5. How does the domain and range change if the graph extends beyond \(x = 5\) or \(x = -5\)?

**Tip**: When interpreting graphs, always check where the function intersects the axes, as this provides crucial information for solving equations involving roots and intercepts.

Use the graph to determine a. the​ function's domain; b. the​ function's range; c. the​ x-intercepts, if​ any; d. the​ y-intercept, if​ any; and e. the missing function​ values, indicated by question​ marks, below.
f(−2)=​? f(2)=​?

Determine the domain, range, x-intercepts, y-intercept, and specific function values using the provided graph. Analyze how f(x) behaves based on its visual representation. Suitable for students in Grades 9-12.

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