Use a graphing calculator to graph the original function y=12x−4

Question

and the vertically dilated function with a factor k=6
. Determine the x-intercepts of both functions.(1 point)
Responses

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 left parenthesis 8 comma 0 right parenthesis , and the dilated function has an x -intercept of left parenthesis 48 comma 0 right parenthesis .

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 left parenthesis negative 8 comma 0 right parenthesis , and the dilated function has an x -intercept of left parenthesis negative 8 comma 0 right parenthesis .

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 left parenthesis 8 comma 0 right parenthesis , and the dilated function has an x -intercept of left parenthesis 8 comma 0 right parenthesis .

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 left parenthesis 0 comma negative 4 right parenthesis , and the dilated function has an x -intercept of left parenthesis 0 comma negative 24 right parenthesis .

Answer 1

To find the x-intercepts of the functions \( y = 12x - 4 \) and the vertically dilated function, we need to determine where each function equals zero.

1. Original Function: \[ y = 12x - 4 \] Set \( y \) to 0 to find the x-intercept: \[ 0 = 12x - 4 \] \[ 12x = 4 \] \[ x = \frac{4}{12} = \frac{1}{3} \]

   So, the x-intercept of the original function is \( \left( \frac{1}{3}, 0 \right) \).

2. Vertically Dilated Function: The vertically dilated function by a factor \( k = 6 \) would be: \[ y = 6(12x - 4) = 72x - 24 \] Set \( y \) to 0 to find the x-intercept: \[ 0 = 72x - 24 \] \[ 72x = 24 \] \[ x = \frac{24}{72} = \frac{1}{3} \]

   So, the x-intercept of the dilated function is also \( \left( \frac{1}{3}, 0 \right) \).

Based on our calculations, the x-intercepts for both functions are the same: \[ \left( \frac{1}{3}, 0 \right) \]

Therefore, none of the provided response options are correct. The x-intercepts for both functions are at \( \left( \frac{1}{3}, 0 \right) \).