Question

Which of the following responses describes transformation(s) of the function h(x)=−16|x|
?(1 point)
Responses

a vertical stretch by a factor of 6
a vertical stretch by a factor of 6

a reflection across the x-axis and a vertical stretch by a factor of 6
a reflection across the x -axis and a vertical stretch by a factor of 6

a reflection across the x-axis and a vertical compression by a factor of 16
a reflection across the x -axis and a vertical compression by a factor of 1 sixth

a vertical compression by a factor of 16

Answer 1

The function given is \( h(x) = -16 |x| \).

To analyze the transformations:

1. The negative sign in front of the \( 16 \) indicates a reflection across the x-axis.
2. The coefficient \( 16 \) indicates a vertical stretch by a factor of \( 16 \).

None of the provided options specify the right combination, but the closest response would be:

**a reflection across the x-axis and a vertical stretch by a factor of 16.**

However, it's important to note that there is no option given that correctly indicates a vertical stretch by a factor of 16. If "6" was meant to reflect the correct factor (though that still would be incorrect), the intended answer might instead be to indicate a vertical stretch of \( 16 \). So it's essential to ensure what is being communicated matches \( -16 |x| \) particularly about the factors involved.

None of the listed options exactly represent the transformations accurately.