Function Transformations Quick Check

Question

5 of 55 of 5 Items

Question
Which of the following correctly identifies the transformations undergone from f(x)=x2
to 4f(x+3)=4(x+3)2
?(1 point)
Responses

translated to the right and stretched vertically
translated to the right and stretched vertically

translated to the right and compressed vertically
translated to the right and compressed vertically

translated to the left and compressed vertically
translated to the left and compressed vertically

translated to the left and stretched vertically

Answer 1

To analyze the transformation from \( f(x) = x^2 \) to \( 4f(x+3) = 4(x+3)^2 \), we can break it down step by step:

1. Start with \( f(x) = x^2 \): This is our basic function.

2. Inside the function, we have \( f(x+3) \): This indicates a horizontal transformation. The \( +3 \) means the function is translated to the left by 3 units.

3. The \( 4f(x+3) \) part means we are stretching the function vertically by a factor of 4. This affects the steepness of the parabola.

Combining these transformations, we see that:

• The function is translated to the left by 3 units (due to \( +3 \) inside the function).
• The function is stretched vertically by a factor of 4 (due to the 4 multiplying the function).

Thus, the correct answer is:

translated to the left and stretched vertically.