Question

Use a graphing calculator to graph the original function y=1/2x−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

Choose the first option: The original and dilated functions both have x-intercept (8, 0).

Work:
Original: (1/2)x − 4 = 0 → x = 8 → (8,0).
Dilated: y = 6[(1/2)x − 4] = 3x − 24; 3x − 24 = 0 → x = 8 → (8,0).

A vertical dilation multiplies y-values, so x-intercepts (where y = 0) stay the same (unless the factor is 0).