Question
Use a graphing calculator to graph the original function y=1/2x−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 find the x-intercepts of the functions given, we need to set \( y = 0 \) and solve for \( x \).
1. **Original function**: \( y = \frac{1}{2}x - 4 \)
- Set \( y = 0 \):
\[
0 = \frac{1}{2}x - 4
\]
- Solve for \( x \):
\[
\frac{1}{2}x = 4 \quad \Rightarrow \quad x = 4 \times 2 = 8
\]
- Thus, the x-intercept of the original function is \( (8, 0) \).
2. **Vertically dilated function** with a factor of \( k = 6 \):
- The equation transforms to \( y = k \cdot \left(\frac{1}{2}x - 4\right) = 6 \cdot \left(\frac{1}{2}x - 4\right) \) or \( y = 3x - 24 \).
- Set \( y = 0 \):
\[
0 = 3x - 24
\]
- Solve for \( x \):
\[
3x = 24 \quad \Rightarrow \quad x = \frac{24}{3} = 8
\]
- Thus, the x-intercept of the dilated function is also \( (8, 0) \).
Therefore, both functions have the same x-intercept:
**Original function**: \( (8, 0) \)
**Dilated function**: \( (8, 0) \)
The correct response is:
"The original function has an x-intercept of (8,0), and the dilated function has an x-intercept of (8,0)."
1. **Original function**: \( y = \frac{1}{2}x - 4 \)
- Set \( y = 0 \):
\[
0 = \frac{1}{2}x - 4
\]
- Solve for \( x \):
\[
\frac{1}{2}x = 4 \quad \Rightarrow \quad x = 4 \times 2 = 8
\]
- Thus, the x-intercept of the original function is \( (8, 0) \).
2. **Vertically dilated function** with a factor of \( k = 6 \):
- The equation transforms to \( y = k \cdot \left(\frac{1}{2}x - 4\right) = 6 \cdot \left(\frac{1}{2}x - 4\right) \) or \( y = 3x - 24 \).
- Set \( y = 0 \):
\[
0 = 3x - 24
\]
- Solve for \( x \):
\[
3x = 24 \quad \Rightarrow \quad x = \frac{24}{3} = 8
\]
- Thus, the x-intercept of the dilated function is also \( (8, 0) \).
Therefore, both functions have the same x-intercept:
**Original function**: \( (8, 0) \)
**Dilated function**: \( (8, 0) \)
The correct response is:
"The original function has an x-intercept of (8,0), and the dilated function has an x-intercept of (8,0)."