To answer your questions, I will break them down based on the information you’ve provided.

Part 1:

a. For how many values of x is f(x) = -5?

From the points listed, we see that the point (2, -5) corresponds to $f(x) = -5$, and that appears to be the only point where this happens. Therefore, there is 1 x-value where $f(x) = -5$.

Answer: 1

Part 2:

b. What is the value of $f(7)$?

You haven’t provided a point where $x = 7$ directly, but you can estimate the value of $f(7)$ based on the graph and the points near $x = 7$. According to the points you've given, the closest ones are:

• (5, -1)
• (8, -1)

Since $x = 7$ lies between 5 and 8, and the y-values at $x = 5$ and $x = 8$ are both -1, we can infer that $f(7) = -1$.

Answer: $f(7) = -1$

---

Would you like further details or have any questions on this?

Here are 5 related questions for further exploration:

1. What does it mean for a function to be continuous between two points like $x = 5$ and $x = 8$?
2. How do you determine the domain and range of a function from a graph?
3. How would you find the value of $f(x)$ at a specific point if the graph has sharp turns or discontinuities?
4. What is the concept of a local maximum or minimum on a graph of a function?
5. How can you identify the symmetry of a function on a graph?

Tip: When estimating values of a function at points that aren’t explicitly given, look at the surrounding values to help you make an educated guess!