Question
The point (4,1) is reflected in the y-axis. What are the coordinates of its image?(1 point)
Responses
(1,-4)
(1,-4)
(-6,2)
(-6,2)
(-4,1)
(-4,1)
(4,1)
When reflecting a figure across the y-axis, which coordinate(s) remain the same? (1 point)
Responses
x-coordinate
x-coordinate
y-coordinates
y-coordinates
inverse coordinates
inverse coordinates
polar coordinates
The funcation y = x^2 + 2
undergoes a reflection. Which of the following could NOT represent f
' (x), the image of f
after the reflection?(1 point)
Responses
y = x^2
y = x^2
160
160
y =− x^2
y =− x^2
y = x^2−4x + 5
Find g(x), which is a reflection over the y-axis of f(x)= x^2 − x
.(1 point)
Responses
g(x) = −x^2 + 7x
g(x) = −x^2 + 7x
g(x) = −x^2 + x
g(x) = −x^2 + x
g(x) = x^2 + x
g(x) = x^2 + x
g(x) = 6x^2
Responses
(1,-4)
(1,-4)
(-6,2)
(-6,2)
(-4,1)
(-4,1)
(4,1)
When reflecting a figure across the y-axis, which coordinate(s) remain the same? (1 point)
Responses
x-coordinate
x-coordinate
y-coordinates
y-coordinates
inverse coordinates
inverse coordinates
polar coordinates
The funcation y = x^2 + 2
undergoes a reflection. Which of the following could NOT represent f
' (x), the image of f
after the reflection?(1 point)
Responses
y = x^2
y = x^2
160
160
y =− x^2
y =− x^2
y = x^2−4x + 5
Find g(x), which is a reflection over the y-axis of f(x)= x^2 − x
.(1 point)
Responses
g(x) = −x^2 + 7x
g(x) = −x^2 + 7x
g(x) = −x^2 + x
g(x) = −x^2 + x
g(x) = x^2 + x
g(x) = x^2 + x
g(x) = 6x^2
Answers
GPT-4o mini
Let's go through each question one by one.
1. **The point (4,1) is reflected in the y-axis. What are the coordinates of its image?**
- When a point \((x, y)\) is reflected across the y-axis, its new coordinates become \((-x, y)\).
- Thus, the reflection of \((4, 1)\) across the y-axis is \((-4, 1)\).
**Answer:** (-4,1)
2. **When reflecting a figure across the y-axis, which coordinate(s) remain the same?**
- In a reflection across the y-axis, the x-coordinate changes sign (it becomes \(-x\)), while the y-coordinate remains the same.
**Answer:** y-coordinates
3. **The function \(y = x^2 + 2\) undergoes a reflection. Which of the following could NOT represent \(f'(x)\), the image of \(f\) after the reflection?**
- A reflection across the x-axis would change the sign in front of the entire function, resulting in \(y = -x^2 - 2\).
- A reflection across the y-axis would result in \(y = x^2 + 2\), which is the same as the original function.
- The options given are examining various forms of reflections. The option that could NOT represent a reflection across either axis would be a constant (like \(y = 160\)), as it does not relate to the quadratic nature of the original function.
**Answer:** 160
4. **Find \(g(x)\), which is a reflection over the y-axis of \(f(x) = x^2 - x\).**
- Reflecting \(f(x)\) over the y-axis means replacing \(x\) with \(-x\):
\[
g(x) = f(-x) = (-x)^2 - (-x) = x^2 + x.
\]
**Answer:** g(x) = x^2 + x
So, the complete answers are:
1. (-4, 1)
2. y-coordinates
3. 160
4. g(x) = x^2 + x
1. **The point (4,1) is reflected in the y-axis. What are the coordinates of its image?**
- When a point \((x, y)\) is reflected across the y-axis, its new coordinates become \((-x, y)\).
- Thus, the reflection of \((4, 1)\) across the y-axis is \((-4, 1)\).
**Answer:** (-4,1)
2. **When reflecting a figure across the y-axis, which coordinate(s) remain the same?**
- In a reflection across the y-axis, the x-coordinate changes sign (it becomes \(-x\)), while the y-coordinate remains the same.
**Answer:** y-coordinates
3. **The function \(y = x^2 + 2\) undergoes a reflection. Which of the following could NOT represent \(f'(x)\), the image of \(f\) after the reflection?**
- A reflection across the x-axis would change the sign in front of the entire function, resulting in \(y = -x^2 - 2\).
- A reflection across the y-axis would result in \(y = x^2 + 2\), which is the same as the original function.
- The options given are examining various forms of reflections. The option that could NOT represent a reflection across either axis would be a constant (like \(y = 160\)), as it does not relate to the quadratic nature of the original function.
**Answer:** 160
4. **Find \(g(x)\), which is a reflection over the y-axis of \(f(x) = x^2 - x\).**
- Reflecting \(f(x)\) over the y-axis means replacing \(x\) with \(-x\):
\[
g(x) = f(-x) = (-x)^2 - (-x) = x^2 + x.
\]
**Answer:** g(x) = x^2 + x
So, the complete answers are:
1. (-4, 1)
2. y-coordinates
3. 160
4. g(x) = x^2 + x