Question

Use a graphing calculator to graph the original function y=12x−4
and the vertically dilated function with a factor k=6
. Determine the x-intercepts of both functions.(1 point)

The original function has an x-intercept of (−8,0)
, and the dilated function has an x-intercept of (−8,0)
.

The original function has an x-intercept of (8,0)
, and the dilated function has an x-intercept of (48,0)
.

The original function has an x-intercept of (0,−4)
, and the dilated function has an x-intercept of (0,−24)
.

The original function has an x-intercept of (8,0)
, and the dilated function has an x-intercept of (8,0)
.

Answer 1

Find x-intercepts by setting y = 0.

Original: 0 = 12x − 4 → x = 4/12 = 1/3, so x-intercept is (1/3, 0).

Dilated by k = 6: y = 6(12x − 4) = 72x − 24. Set 0 = 72x − 24 → x = 24/72 = 1/3, so x-intercept is also (1/3, 0).

A vertical dilation about the x-axis does not change x-intercepts. None of the provided multiple-choice options show (1/3, 0) for the intercept, so none are correct.