https://file.aiquickdraw.com/mathbot/file/1726954604409e657txwm.jpg

Let's break down the problem using the table of function values provided in the image.

### Table:
\[
\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
\hline
f(x) & 93 & 34 & -19 & 42 & -80 & 60 & -78 & -85 & 73 & 12 \\
\hline
\end{array}
\]

#### 1. Evaluate \( f(4) \):
To evaluate \( f(4) \), look at the row for \( x = 4 \). According to the table:
\[
f(4) = -80
\]

#### 2. Determine \( x \) when \( f(x) = -19 \):
Now, we need to find \( x \) such that \( f(x) = -19 \). By examining the table:
\[
f(2) = -19
\]
So, \( x = 2 \) when \( f(x) = -19 \).

### Answers:
- \( f(4) = -80 \)
- \( x = 2 \) when \( f(x) = -19 \)

Do you need any more clarification on this? 

Here are 5 questions to further expand on the concept of evaluating functions:
1. How would you describe a function in mathematical terms?
2. Can you give an example of a real-world situation that can be modeled by a function?
3. What does it mean for a function to be "evaluated" at a specific value of \( x \)?
4. What is the difference between finding \( f(x) \) and solving for \( x \) given \( f(x) \)?
5. Can you explain how you would find \( x \) if the function table wasn't available but you had the function equation?

**Tip:** When working with function tables, be careful with the negative values, both for \( x \) and \( f(x) \), as they can affect how you interpret results.

Use the table to answer the following questions: Evaluate f(4) and determine x when f(x) = -19.

Learn how to evaluate functions using a function table. In this problem, we calculate f(4) and determine x when f(x) = -19 using provided data. Suitable for Grades 7-9.

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