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)
.
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 .
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Answer 1

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

### 1. Finding the x-intercept of the original function:

The x-intercept occurs where \( y = 0 \).

Set the equation to zero:

\[ 0 = 12x - 4 \]

Now solve for \( x \):

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

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

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### 2. Finding the x-intercept of the vertically dilated function:

The vertically dilated function is given by:

\[ y = k(12x - 4) = 6(12x - 4) = 72x - 24 \]

Now, we find the x-intercept of the dilated function by setting \( y = 0 \):

\[ 0 = 72x - 24 \]

Solving for \( x \):

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

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

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### Conclusion:

The x-intercepts for both functions are the same:

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

**None of the provided response options correctly reflect these results, as they mention (8,0) or other values that are not accurate.**