Question

Stretch the function horizontally by a factor of 4, reflect it with respect to the x-axis, and move it 2 units down.

a) y = f(4x) - 2
b) y = -f(4x) - 2
c) y = f(4x) + 2
d) y = -f(4x) + 2

Answer 1

To stretch the function horizontally by a factor of 4, reflect it with respect to the x-axis, and move it 2 units down, the correct answer is y = -f(4x) - 2.

Step-by-step explanation:

To stretch the function horizontally by a factor of 4, reflect it with respect to the x-axis, and move it 2 units down, we need to apply the transformations in the correct order.

First, we multiply the input by 4, which stretches the function horizontally. This can be represented as f(4x). Next, we reflect the function with respect to the x-axis, which can be represented as -f(4x). Finally, we move the function 2 units down, which can be represented as -f(4x) - 2.

Therefore, the correct answer is y = -f(4x) - 2 (option b).