Question
se the image to answer the question.
A coordinate plane's x-axis ranges from negative 9 to 9 and its y-axis ranges from negative 11 to 11, both by 1-unit increments. A line with arrows at both ends labeled f of x equals x plus 2 is plotted passing through 7 marked points.
Given the graph of the function f(x)=x+2
, which set of ordered pairs would be used to create the graph of the inverse?
(1 point)
Responses
{(−1,−3),(0,−2),(−1,1),(2,0),(3,1),(4,2),(5,3)}
left brace left parenthesis negative 1 comma negative 3 right parenthesis comma left parenthesis 0 comma negative 2 right parenthesis comma left parenthesis negative 1 comma 1 right parenthesis comma left parenthesis 2 comma 0 right parenthesis comma left parenthesis 3 comma 1 right parenthesis comma left parenthesis 4 comma 2 right parenthesis comma left parenthesis 5 comma 3 right parenthesis right brace
{(−1,−2),(0,−2),(1,−1),(2,0),(3,1),(4,2),(5,3)}
left brace left parenthesis negative 1 comma negative 2 right parenthesis comma left parenthesis 0 comma negative 2 right parenthesis comma left parenthesis 1 comma negative 1 right parenthesis comma left parenthesis 2 comma 0 right parenthesis comma left parenthesis 3 comma 1 right parenthesis comma left parenthesis 4 comma 2 right parenthesis comma left parenthesis 5 comma 3 right parenthesis right brace
{(−1,−3),(0,−2),(1,−1),(2,0),(3,1),(4,2),(5,3)}
left brace left parenthesis negative 1 comma negative 3 right parenthesis comma left parenthesis 0 comma negative 2 right parenthesis comma left parenthesis 1 comma negative 1 right parenthesis comma left parenthesis 2 comma 0 right parenthesis comma left parenthesis 3 comma 1 right parenthesis comma left parenthesis 4 comma 2 right parenthesis comma left parenthesis 5 comma 3 right parenthesis right brace
{(−1,−3),(0,−2),(1,−1),(2,0),(3,1),(2,4),(5,3)}
A coordinate plane's x-axis ranges from negative 9 to 9 and its y-axis ranges from negative 11 to 11, both by 1-unit increments. A line with arrows at both ends labeled f of x equals x plus 2 is plotted passing through 7 marked points.
Given the graph of the function f(x)=x+2
, which set of ordered pairs would be used to create the graph of the inverse?
(1 point)
Responses
{(−1,−3),(0,−2),(−1,1),(2,0),(3,1),(4,2),(5,3)}
left brace left parenthesis negative 1 comma negative 3 right parenthesis comma left parenthesis 0 comma negative 2 right parenthesis comma left parenthesis negative 1 comma 1 right parenthesis comma left parenthesis 2 comma 0 right parenthesis comma left parenthesis 3 comma 1 right parenthesis comma left parenthesis 4 comma 2 right parenthesis comma left parenthesis 5 comma 3 right parenthesis right brace
{(−1,−2),(0,−2),(1,−1),(2,0),(3,1),(4,2),(5,3)}
left brace left parenthesis negative 1 comma negative 2 right parenthesis comma left parenthesis 0 comma negative 2 right parenthesis comma left parenthesis 1 comma negative 1 right parenthesis comma left parenthesis 2 comma 0 right parenthesis comma left parenthesis 3 comma 1 right parenthesis comma left parenthesis 4 comma 2 right parenthesis comma left parenthesis 5 comma 3 right parenthesis right brace
{(−1,−3),(0,−2),(1,−1),(2,0),(3,1),(4,2),(5,3)}
left brace left parenthesis negative 1 comma negative 3 right parenthesis comma left parenthesis 0 comma negative 2 right parenthesis comma left parenthesis 1 comma negative 1 right parenthesis comma left parenthesis 2 comma 0 right parenthesis comma left parenthesis 3 comma 1 right parenthesis comma left parenthesis 4 comma 2 right parenthesis comma left parenthesis 5 comma 3 right parenthesis right brace
{(−1,−3),(0,−2),(1,−1),(2,0),(3,1),(2,4),(5,3)}
Answers
GPT-4o mini
To find the inverse of the function \( f(x) = x + 2 \), we need to switch the x and y coordinates of the ordered pairs from the original function. The function \( f(x) = x + 2 \) has the property that for each ordered pair \( (x, y) \), the corresponding inverse ordered pair will be \( (y, x) \).
From \( f(x) = x + 2 \), we can find several points on the graph:
1. If \( x = -2 \), then \( f(-2) = 0 \) → point \( (-2, 0) \)
2. If \( x = -1 \), then \( f(-1) = 1 \) → point \( (-1, 1) \)
3. If \( x = 0 \), then \( f(0) = 2 \) → point \( (0, 2) \)
4. If \( x = 1 \), then \( f(1) = 3 \) → point \( (1, 3) \)
5. If \( x = 2 \), then \( f(2) = 4 \) → point \( (2, 4) \)
6. If \( x = 3 \), then \( f(3) = 5 \) → point \( (3, 5) \)
7. If \( x = 4 \), then \( f(4) = 6 \) → point \( (4, 6) \)
8. If \( x = 5 \), then \( f(5) = 7 \) → point \( (5, 7) \)
9. If \( x = 6 \), then \( f(6) = 8 \) → point \( (6, 8) \)
The pairs \( (x, f(x)) \) could be:
- For \( x = -2 \), \( y = 0 \) → ordered pair is \( (-2, 0) \)
- For \( x = -1 \), \( y = 1 \) → ordered pair is \( (-1, 1) \)
- For \( x = 0 \), \( y = 2 \) → ordered pair is \( (0, 2) \)
- For \( x = 1 \), \( y = 3 \) → ordered pair is \( (1, 3) \)
- For \( x = 2 \), \( y = 4 \) → ordered pair is \( (2, 4) \)
- For \( x = 3 \), \( y = 5 \) → ordered pair is \( (3, 5) \)
To find the inverse ordered pairs, we exchange the coordinates to get:
- From \( (-2, 0) \) we get \( (0, -2) \)
- From \( (-1, 1) \) we get \( (1, -1) \)
- From \( (0, 2) \) we get \( (2, 0) \)
- From \( (1, 3) \) we get \( (3, 1) \)
- From \( (2, 4) \) we get \( (4, 2) \)
- From \( (3, 5) \) we get \( (5, 3) \)
Now comparing the provided options, we see that the correct option, which lists the ordered pairs needed to create the inverse, is:
\[
\{(−1,−3),(0,−2),(1,−1),(2,0),(3,1),(4,2),(5,3)\}
\]
This is the set that reflects the coordinates properly and fulfills the inverse relationship.
From \( f(x) = x + 2 \), we can find several points on the graph:
1. If \( x = -2 \), then \( f(-2) = 0 \) → point \( (-2, 0) \)
2. If \( x = -1 \), then \( f(-1) = 1 \) → point \( (-1, 1) \)
3. If \( x = 0 \), then \( f(0) = 2 \) → point \( (0, 2) \)
4. If \( x = 1 \), then \( f(1) = 3 \) → point \( (1, 3) \)
5. If \( x = 2 \), then \( f(2) = 4 \) → point \( (2, 4) \)
6. If \( x = 3 \), then \( f(3) = 5 \) → point \( (3, 5) \)
7. If \( x = 4 \), then \( f(4) = 6 \) → point \( (4, 6) \)
8. If \( x = 5 \), then \( f(5) = 7 \) → point \( (5, 7) \)
9. If \( x = 6 \), then \( f(6) = 8 \) → point \( (6, 8) \)
The pairs \( (x, f(x)) \) could be:
- For \( x = -2 \), \( y = 0 \) → ordered pair is \( (-2, 0) \)
- For \( x = -1 \), \( y = 1 \) → ordered pair is \( (-1, 1) \)
- For \( x = 0 \), \( y = 2 \) → ordered pair is \( (0, 2) \)
- For \( x = 1 \), \( y = 3 \) → ordered pair is \( (1, 3) \)
- For \( x = 2 \), \( y = 4 \) → ordered pair is \( (2, 4) \)
- For \( x = 3 \), \( y = 5 \) → ordered pair is \( (3, 5) \)
To find the inverse ordered pairs, we exchange the coordinates to get:
- From \( (-2, 0) \) we get \( (0, -2) \)
- From \( (-1, 1) \) we get \( (1, -1) \)
- From \( (0, 2) \) we get \( (2, 0) \)
- From \( (1, 3) \) we get \( (3, 1) \)
- From \( (2, 4) \) we get \( (4, 2) \)
- From \( (3, 5) \) we get \( (5, 3) \)
Now comparing the provided options, we see that the correct option, which lists the ordered pairs needed to create the inverse, is:
\[
\{(−1,−3),(0,−2),(1,−1),(2,0),(3,1),(4,2),(5,3)\}
\]
This is the set that reflects the coordinates properly and fulfills the inverse relationship.