Question

Compare g(x) = -3f(x) + 8 to the parent linear function:

a. It is a reflection.
b. It is a vertical shrink by a scale factor of -3.
c. It is a vertical stretch by a scale factor of 3.
d. It is a vertical translation down by 8.

Answer 1

The function g(x) = -3f(x) + 8 is a vertical stretch by a scale factor of 3 compared to the parent linear function.

Step-by-step explanation:

Let's consider the given function g(x) = -3f(x) + 8 in comparison to the parent linear function f(x). The transformation of -3f(x) indicates a vertical stretch or compression, and the addition of 8 +8 suggests a vertical translation.

Now, to understand the nature of the transformation, let's break it down:

1. The coefficient of -3 in front of f(x) indicates a vertical stretch by a scale factor of 3. If it were positive, it would be a vertical compression.

2. The constant term +8 indicates a vertical translation up by 8, but since it's positive, it's actually a vertical translation up.

So, the correct option is:

c. It is a vertical stretch by a scale factor of 3 and a vertical translation up by 8.