Question
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 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)}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 2 comma 4 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 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
Answers
Answered by
GPT-4o mini
To find the ordered pairs that would create the graph of the inverse function of \( f(x) = x + 2 \), we need to first determine the inverse function.
1. The function is defined as \( f(x) = x + 2 \).
2. To find the inverse, we switch \( x \) and \( y \):
\[
y = x + 2 \implies x = y + 2 \implies y = x - 2
\]
Thus, the inverse function is \( f^{-1}(x) = x - 2 \).
Next, we need to find the ordered pairs that represent the inverse function:
- \( f^{-1}(-1) = -1 - 2 = -3 \) → \( (-1, -3) \)
- \( f^{-1}(0) = 0 - 2 = -2 \) → \( (0, -2) \)
- \( f^{-1}(1) = 1 - 2 = -1 \) → \( (1, -1) \)
- \( f^{-1}(2) = 2 - 2 = 0 \) → \( (2, 0) \)
- \( f^{-1}(3) = 3 - 2 = 1 \) → \( (3, 1) \)
- \( f^{-1}(4) = 4 - 2 = 2 \) → \( (4, 2) \)
- \( f^{-1}(5) = 5 - 2 = 3 \) → \( (5, 3) \)
Now the ordered pairs for the inverse function are \( \{(-1, -3), (0, -2), (1, -1), (2, 0), (3, 1), (4, 2), (5, 3)\} \).
Looking at the provided options, the correct set of ordered pairs is:
\[
\{(-1, -3), (0, -2), (1, -1), (2, 0), (3, 1), (4, 2), (5, 3)\}
\]
1. The function is defined as \( f(x) = x + 2 \).
2. To find the inverse, we switch \( x \) and \( y \):
\[
y = x + 2 \implies x = y + 2 \implies y = x - 2
\]
Thus, the inverse function is \( f^{-1}(x) = x - 2 \).
Next, we need to find the ordered pairs that represent the inverse function:
- \( f^{-1}(-1) = -1 - 2 = -3 \) → \( (-1, -3) \)
- \( f^{-1}(0) = 0 - 2 = -2 \) → \( (0, -2) \)
- \( f^{-1}(1) = 1 - 2 = -1 \) → \( (1, -1) \)
- \( f^{-1}(2) = 2 - 2 = 0 \) → \( (2, 0) \)
- \( f^{-1}(3) = 3 - 2 = 1 \) → \( (3, 1) \)
- \( f^{-1}(4) = 4 - 2 = 2 \) → \( (4, 2) \)
- \( f^{-1}(5) = 5 - 2 = 3 \) → \( (5, 3) \)
Now the ordered pairs for the inverse function are \( \{(-1, -3), (0, -2), (1, -1), (2, 0), (3, 1), (4, 2), (5, 3)\} \).
Looking at the provided options, the correct set of ordered pairs is:
\[
\{(-1, -3), (0, -2), (1, -1), (2, 0), (3, 1), (4, 2), (5, 3)\}
\]
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