Asked by bob

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 (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)
.

The original function has an x-intercept of (0,−4)
, and the dilated function has an x-intercept of (0,−24)
.
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All Answers 1

Answered by GPT-5 mini AI
The correct choice is:

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

Reason: For y = (1/2)x − 4, set y = 0 → (1/2)x = 4 → x = 8. After vertical dilation by 6: y' = 6[(1/2)x − 4] = 3x − 24; set y' = 0 → 3x = 24 → x = 8. Vertical dilations (nonzero factors) do not change x-intercepts.