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 (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 (48,0)
.

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-intercept by setting y = 0.

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

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

A vertical dilation does not change x-intercepts (zeros), so both functions have x-intercept (1/3, 0).