https://file.aiquickdraw.com/mathbot/file/1726460982485a2ingr2p.jpg

Let's analyze the graph and answer the questions provided.

### A) Domain of \( f(x) \):
The **domain** is the set of all possible input values (x-values) for which the function is defined. Looking at the graph, the function extends infinitely to the left and right, meaning the function is defined for all real numbers except at \( x = -2 \), where there is a vertical asymptote.

**Answer:**
The domain of \( f(x) \) is \( (-\infty, -2) \cup (-2, \infty) \).

### B) Range of \( f(x) \):
The **range** is the set of all possible output values (y-values). The function approaches negative infinity as \( x \) moves left or right, but there's a lower boundary around \( y = -8 \) where the graph doesn't go below. The graph also approaches positive infinity at the vertical asymptote but appears to be bounded above, around \( y = 8 \).

**Answer:**
The range of \( f(x) \) is approximately \( [-8, 8] \).

### C) \( x \)-Intercepts:
The **x-intercepts** are points where the graph crosses the x-axis, i.e., where \( f(x) = 0 \). By observing the graph, we can see that the graph crosses the x-axis at two points: \( x = -5 \) and \( x = 2 \).

**Answer:**
The x-intercepts are \( (-5, 0) \) and \( (2, 0) \).

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Do you want further details or have any questions?

Here are 5 related questions for further practice:
1. What are the \( y \)-intercepts of \( f(x) \)?
2. Identify the intervals where \( f(x) \) is increasing or decreasing.
3. What is the behavior of \( f(x) \) near the vertical asymptote at \( x = -2 \)?
4. Find the coordinates of the local maximum and minimum points.
5. Does the function have any symmetry (odd, even, or neither)?

**Tip:** When dealing with vertical asymptotes, always check for undefined values in the function's domain, which may cause discontinuities.

The graph of y = f(x) is given below. Answer each of the questions below the graph. A) What is the domain of f(x)? Give your answer using interval notation. B) What is the range of f(x)? Give your answer using interval notation. C) What is/are the x-intercepts of f(x)?

Explore how to find the domain, range, and x-intercepts of a function by analyzing its graph. This example includes concepts like vertical asymptotes and solutions for x-intercepts. Ideal for students in Grades 10-12.

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