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) Responses
A. The original function has an x-intercept of (−8,0), and the dilated function has an x-intercept of (−8,0).
B. The original function has an x-intercept of (8,0), and the dilated function has an x-intercept of (48,0).
C. The original function has an x-intercept of (8,0), and the dilated function has an x-intercept of (8,0).
D. The original function has an x-intercept of (0,−4), and the dilated function has an x-intercept of (0,−24)
CHOOSE ONE OF THESE RESPONSES
To determine the x-intercepts of a function, we set y equal to zero and solve for x.
For the original function y = 12x - 4:
0 = 12x - 4
12x = 4
x = 4/12
x = 1/3
So the x-intercept of the original function is (1/3, 0).
For the dilated function y = 6(12x - 4):
0 = 6(12x - 4)
0 = 72x - 24
72x = 24
x = 24/72
x = 1/3
So the x-intercept of the dilated function is also (1/3, 0).
Therefore, the correct answer is:
C. The original function has an x-intercept of (1/3, 0), and the dilated function has an x-intercept of (1/3, 0).