Question
page 8 of 9
Question 1
A)Create a table for the reflection over the x-axis of the function f(x)=(x−1)2.(2 points)
x 0 1 2
−f(x) $$ $$ $$
Question 2
A)
Based on the following tables, which of the following options is a true description of the graphs of f(x) and g(x)?
x
f(x)
−2
−6
0 −4
2 −2
4 0
x
g(x)
−2
6
0 4
2 2
4 0
Option #1: One graph is a reflection of the other over the x-axis.
Option #2: One graph is a reflection of the other over the y-axis.
Option #3: One graph is a reflection of the other about the origin.
(1 point)
Option #$$
Question 3
A)
If the point (3,4) is on the graph of y=f(x), what point must be on the graph of y=−f(x)?
Option #1: (−3,4)
Option #2: (−3,−4)
Option #3: (3,−4)
(1 point)
The point in option #$$ must be on the graph of y=−f(x).
Question 4
A)
Use the image to answer the question.
Given the graph of f(x)=(x+3)2, which of the options is the graph of y=−f(x)?
(1 point)
The graph of y=−f(x) is option $$.
Question 5
A)
Use the image to answer the question.
Given the graph of y=f(x), which of the following options is the graph of y=−f(x)? Enter the option number of the correct answer.
Option #1: Graph B
Option #2: Graph C
Option #3: Graph D
(1 point)
Option #$$
Question 1
A)Create a table for the reflection over the x-axis of the function f(x)=(x−1)2.(2 points)
x 0 1 2
−f(x) $$ $$ $$
Question 2
A)
Based on the following tables, which of the following options is a true description of the graphs of f(x) and g(x)?
x
f(x)
−2
−6
0 −4
2 −2
4 0
x
g(x)
−2
6
0 4
2 2
4 0
Option #1: One graph is a reflection of the other over the x-axis.
Option #2: One graph is a reflection of the other over the y-axis.
Option #3: One graph is a reflection of the other about the origin.
(1 point)
Option #$$
Question 3
A)
If the point (3,4) is on the graph of y=f(x), what point must be on the graph of y=−f(x)?
Option #1: (−3,4)
Option #2: (−3,−4)
Option #3: (3,−4)
(1 point)
The point in option #$$ must be on the graph of y=−f(x).
Question 4
A)
Use the image to answer the question.
Given the graph of f(x)=(x+3)2, which of the options is the graph of y=−f(x)?
(1 point)
The graph of y=−f(x) is option $$.
Question 5
A)
Use the image to answer the question.
Given the graph of y=f(x), which of the following options is the graph of y=−f(x)? Enter the option number of the correct answer.
Option #1: Graph B
Option #2: Graph C
Option #3: Graph D
(1 point)
Option #$$
Answers
GPT-4o mini
Sure! Here’s how to approach each question:
### Question 1
To create a table for the reflection of the function \( f(x)=(x−1)^2 \) over the x-axis, we first need to calculate the values of \(-f(x)\) for the given x-values.
1. **Calculate \( f(x) \)**:
- For \( x = 0 \): \( f(0) = (0-1)^2 = 1 \)
- For \( x = 1 \): \( f(1) = (1-1)^2 = 0 \)
- For \( x = 2 \): \( f(2) = (2-1)^2 = 1 \)
2. **Calculate \(-f(x)\)**:
- For \( x = 0 \): \(-f(0) = -1\)
- For \( x = 1 \): \(-f(1) = 0\)
- For \( x = 2 \): \(-f(2) = -1\)
So, the completed table would look like this:
| x | 0 | 1 | 2 |
|---|---|---|---|
| −f(x) | -1 | 0 | -1 |
### Question 2
To find out the relationship between the graphs \( f(x) \) and \( g(x) \), we can analyze the values in both tables:
- \( f(x) \) is negative at \( x = -2 \) and positive at \( x = 0 \).
- \( g(x) \) is positive at \( x = -2 \) and negative at \( x = 0 \).
This indicates that \( g(x) \) is a reflection of \( f(x) \) over the x-axis. Thus, the correct option is:
**Option #1: One graph is a reflection of the other over the x-axis.**
### Question 3
Given the point \( (3,4) \) is on the graph of \( y=f(x) \), it indicates that when \( x=3 \), \( f(3)=4 \).
Now, when considering \( y=-f(x) \):
- The point \( (3, -f(3)) \) would then be \( (3, -4) \).
So, the answer is:
**Option #3: (3,−4)** must be on the graph of \( y=−f(x) \).
### Question 4
For the function \( f(x)=(x+3)^2 \), reflecting this over the x-axis results in \( y=−f(x) = -(x+3)^2 \). The graph of \( y=−f(x) \) would be an upside-down parabola.
Since the question states to select an option, you would need to visually compare the graphs to determine which option depicts an upside-down parabola. Fill in the blank with the option number that matches this description.
### Question 5
Similar to Question 4, you need to visually look at the provided graphs in order to determine which one represents \( y=−f(x) \). You are looking for the graph that is the reflection of \( y=f(x) \) across the x-axis. Again, fill in the blank with the corresponding option number.
If you have access to the graphs mentioned, choose the suitable options based on the reasoning provided.
### Question 1
To create a table for the reflection of the function \( f(x)=(x−1)^2 \) over the x-axis, we first need to calculate the values of \(-f(x)\) for the given x-values.
1. **Calculate \( f(x) \)**:
- For \( x = 0 \): \( f(0) = (0-1)^2 = 1 \)
- For \( x = 1 \): \( f(1) = (1-1)^2 = 0 \)
- For \( x = 2 \): \( f(2) = (2-1)^2 = 1 \)
2. **Calculate \(-f(x)\)**:
- For \( x = 0 \): \(-f(0) = -1\)
- For \( x = 1 \): \(-f(1) = 0\)
- For \( x = 2 \): \(-f(2) = -1\)
So, the completed table would look like this:
| x | 0 | 1 | 2 |
|---|---|---|---|
| −f(x) | -1 | 0 | -1 |
### Question 2
To find out the relationship between the graphs \( f(x) \) and \( g(x) \), we can analyze the values in both tables:
- \( f(x) \) is negative at \( x = -2 \) and positive at \( x = 0 \).
- \( g(x) \) is positive at \( x = -2 \) and negative at \( x = 0 \).
This indicates that \( g(x) \) is a reflection of \( f(x) \) over the x-axis. Thus, the correct option is:
**Option #1: One graph is a reflection of the other over the x-axis.**
### Question 3
Given the point \( (3,4) \) is on the graph of \( y=f(x) \), it indicates that when \( x=3 \), \( f(3)=4 \).
Now, when considering \( y=-f(x) \):
- The point \( (3, -f(3)) \) would then be \( (3, -4) \).
So, the answer is:
**Option #3: (3,−4)** must be on the graph of \( y=−f(x) \).
### Question 4
For the function \( f(x)=(x+3)^2 \), reflecting this over the x-axis results in \( y=−f(x) = -(x+3)^2 \). The graph of \( y=−f(x) \) would be an upside-down parabola.
Since the question states to select an option, you would need to visually compare the graphs to determine which option depicts an upside-down parabola. Fill in the blank with the option number that matches this description.
### Question 5
Similar to Question 4, you need to visually look at the provided graphs in order to determine which one represents \( y=−f(x) \). You are looking for the graph that is the reflection of \( y=f(x) \) across the x-axis. Again, fill in the blank with the corresponding option number.
If you have access to the graphs mentioned, choose the suitable options based on the reasoning provided.