Question

If you apply the changes below to the linear
parent function, f(x) = x, what is the equation
of the new function?
• Vertically stretch by a factor of 4.
• Flip over the x-axis.
0 g(x) =-4x

0 g(x) = -¼x

0 g(x) = ¼x-1

0 g(x) = 11

Answer 1

To determine the equation of the new function after applying the specified transformations to the linear parent function \( f(x) = x \), let's analyze the changes step-by-step:

1. **Vertically stretch by a factor of 4:**
- This means we multiply the function by 4. So, we transform \( f(x) = x \) into \( 4f(x) = 4x \).

2. **Flip over the x-axis:**
- Flipping over the x-axis means we negate the function. Thus, we take \( 4x \) and change it to \( -4x \).

Combining these transformations, we get:
\[
g(x) = -4x
\]

Thus, the equation of the new function is:
\[
g(x) = -4x
\]

So the correct answer is:
- \( g(x) = -4x \)