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The image contains a question about the function \( f(x) \) with given input-output pairs in a table. It then asks which points lie on the function \( g(x) = 3f(x) \). Let's break it down:

Given the table:

\[
\begin{array}{c|c}
x & f(x) \\
\hline
-4 & 2 \\
-3 & 1 \\
-2 & 0 \\
-1 & 1 \\
\end{array}
\]

Now, the function \( g(x) = 3f(x) \). This means the output values of \( g(x) \) are three times the corresponding output values of \( f(x) \). For each \( x \), we calculate \( g(x) \):

- For \( x = -4 \), \( f(-4) = 2 \), so \( g(-4) = 3 \times 2 = 6 \).
- For \( x = -3 \), \( f(-3) = 1 \), so \( g(-3) = 3 \times 1 = 3 \).
- For \( x = -2 \), \( f(-2) = 0 \), so \( g(-2) = 3 \times 0 = 0 \).
- For \( x = -1 \), \( f(-1) = 1 \), so \( g(-1) = 3 \times 1 = 3 \).

Now, we check the points given:

- \( (-12, 6) \) – This is not correct as \( g(x) \) does not have an \( x \)-value of -12.
- \( (-3, 4) \) – This is incorrect because \( g(-3) = 3 \), not 4.
- \( (0, 6) \) – This is incorrect because there is no value for \( f(0) \) in the table.
- \( (-2, 0) \) – This is correct because \( g(-2) = 0 \).
- \( (-1, -2) \) – This is incorrect because \( g(-1) = 3 \), not -2.

The correct point is \( (-2, 0) \).

Do you want more details or have any questions? Here are a few related questions:

1. How would you calculate \( g(x) \) if the table provided additional values for \( f(x) \)?
2. How does the function \( g(x) = 3f(x) \) affect the graph of \( f(x) \)?
3. What is the general rule for transforming a function like \( f(x) \) by a constant factor?
4. If the transformation was \( g(x) = 2f(x) + 1 \), how would that change the points on the graph?
5. How can we find the inverse of the function \( g(x) \)?

**Tip:** Always check the given values in the transformation carefully and apply them to the formula systematically.

If g(x) = 3f(x), which of the following points are on the function g(x)? Select all that apply.

Explore how to find points on the function g(x) = 3f(x) given a table of f(x) values. Learn step-by-step how the transformation affects the function's outputs. Suitable for Grades 8-10.

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