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

Question

𝑦
=
1
2
𝑥
−
4
and the vertically dilated function with a factor k=6
𝑘
=
6
. Determine the x-intercepts of both functions.(1 point)
Responses

The original function has an x-intercept of (8,0)
(
8
,
0
)
, and the dilated function has an x-intercept of (48,0)
(
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 (0,−4)
(
0
,
−
4
)
, and the dilated function has an x-intercept of (0,−24)
(
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 .

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

Answer 1

To analyze the functions and find their x-intercepts, we begin with the original function:

1. Original Function: \[ y = 12x - 4 \]

   To find the x-intercept, we set \( y = 0 \): \[ 0 = 12x - 4 \] Solving for x: \[ 12x = 4 \quad \Rightarrow \quad x = \frac{4}{12} = \frac{1}{3} \] So, the x-intercept of the original function is: \[ \left(\frac{1}{3}, 0\right) \]

2. Vertically Dilated Function: The vertically dilated function with a factor of \( k = 6 \) is: \[ y = 6(12x - 4) = 72x - 24 \]

   To find its x-intercept, we set \( y = 0 \): \[ 0 = 72x - 24 \] Solving for x: \[ 72x = 24 \quad \Rightarrow \quad x = \frac{24}{72} = \frac{1}{3} \] So, the x-intercept of the dilated function is also: \[ \left(\frac{1}{3}, 0\right) \]

Summary of Results:

• The original function has an x-intercept of \( \left(\frac{1}{3}, 0\right) \).
• The dilated function also has an x-intercept of \( \left(\frac{1}{3}, 0\right) \).

It seems like no option with the x-intercepts is provided, but both functions have the same x-intercept at \( \left(\frac{1}{3}, 0\right) \).