We are given the function $f(x) = 5x - 8$ and are tasked with filling in the table based on this function. The table already has $f(-4) = -28$ as shown in the example calculation:

$f(-4) = 5(-4) - 8 = -20 - 8 = -28$

Now, let's calculate the values for $a$, $b$, and $c$ corresponding to $f(-2)$, $f(3)$, and $f(7)$, respectively.

1. For $a = f(-2)$: $f(-2) = 5(-2) - 8 = -10 - 8 = -18$

2. For $b = f(3)$: $f(3) = 5(3) - 8 = 15 - 8 = 7$

3. For $c = f(7)$: $f(7) = 5(7) - 8 = 35 - 8 = 27$

Thus, the completed table should be:

So the values for the dropdowns are:

• $a = -18$
• $b = 7$
• $c = 27$

Let me know if you'd like further explanation!

Here are 5 related questions to extend this problem:

1. How would the values change if the function were $f(x) = 3x - 5$?
2. What is the slope of the function $f(x) = 5x - 8$?
3. What does the $-8$ in the equation represent graphically?
4. How would you find the inverse of the function $f(x) = 5x - 8$?
5. What is the domain and range of this linear function?

Tip: Always start by evaluating a function step by step to avoid mistakes, especially when dealing with negatives or complex expressions.