Question

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

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

Answer 1

To determine the x-intercepts of the original function \( y = 12x - 4 \) and the vertically dilated function with a dilation factor \( k = 6 \), we first find the x-intercept of the original function.

### Original Function:

Set \( y = 0 \):
\[
0 = 12x - 4
\]

Add 4 to both sides:
\[
4 = 12x
\]

Divide by 12:
\[
x = \frac{4}{12} = \frac{1}{3}
\]

Thus, the x-intercept of the original function is:
\[
\left(\frac{1}{3}, 0\right)
\]

### Vertically Dilated Function:

The dilated function can be expressed as:
\[
y = k \cdot (12x - 4) = 6(12x - 4)
\]
Expanding this:
\[
y = 72x - 24
\]

Now, set \( y = 0 \):
\[
0 = 72x - 24
\]

Add 24 to both sides:
\[
24 = 72x
\]

Divide by 72:
\[
x = \frac{24}{72} = \frac{1}{3}
\]

Thus, the x-intercept of the vertically dilated function is also:
\[
\left(\frac{1}{3}, 0\right)
\]

### Conclusion:
Both the original function and the vertically dilated function have the same x-intercept, which is \( \left(\frac{1}{3}, 0\right) \).

None of the provided options correspond to this result, so it seems there may be an error in the given options.