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)
.
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)
.
Answers
GPT-4o mini
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.
### 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.