Question

Analyze the effect on the x- and y-values of the original function f(x)=x3
when it is stretched vertically by a factor of a that is greater than 0 but less than 1. (1 point)
Responses

The x-values increase by a factor of a, and the y-values decrease when multiplied by a factor of a.
The x -values increase by a factor of a , and the y -values decrease when multiplied by a factor of a .

The x-values remain the same, and the y-values increase when multiplied by a factor of a.
The x -values remain the same, and the y -values increase when multiplied by a factor of a .

The x-values decrease when multiplied by a factor of a, and the y- values remain the same.
The x -values decrease when multiplied by a factor of a , and the y - values remain the same.

The x-values remain the same while the magnitudes of the y-values decrease when multiplied by a factor of a.

Answer 1

Correct answer: The x-values remain the same while the magnitudes of the y-values decrease when multiplied by a factor of a.

Reason: A vertical stretch by factor a produces g(x)=a·f(x)=a x^3. This multiplies each y-value by a (0<a<1), so y-values shrink in magnitude while x-values are unchanged.