Question

Use a graphing calculator to graph the original function y=12x−4
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 \( \left(\frac{1}{3}, 0\right) \).