Given the graph of the function f(x)=x+2

Question

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, 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)}
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{(−1,−2),(0,−2),(1,−1),(2,0),(3,1),(4,2),(5,3)}
{
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,
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0
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4
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,
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5
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}
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Answer 1

To find the set of ordered pairs that create the graph of the inverse of the function \( f(x) = x + 2 \), we first need to find the inverse function.

The inverse of a function is found by swapping the roles of \( x \) and \( y \). So we start with:

1. Write the function with \( y \): \[ y = x + 2 \]

2. Swap \( x \) and \( y \): \[ x = y + 2 \]

3. Solve for \( y \): \[ y = x - 2 \]

Thus, the inverse function is \( f^{-1}(x) = x - 2 \).

Next, we can find the ordered pairs for the inverse by taking the original ordered pairs from the function \( f(x) \) and swapping their coordinates.

From the function \( f(x) = x + 2 \), the original ordered pairs might be:

• When \( x = -1 \), \( f(-1) = -1 + 2 = 1 \) → \( (-1, 1) \)
• When \( x = 0 \), \( f(0) = 0 + 2 = 2 \) → \( (0, 2) \)
• When \( x = 1 \), \( f(1) = 1 + 2 = 3 \) → \( (1, 3) \)
• When \( x = 2 \), \( f(2) = 2 + 2 = 4 \) → \( (2, 4) \)
• When \( x = 3 \), \( f(3) = 3 + 2 = 5 \) → \( (3, 5) \)
• When \( x = 4 \), \( f(4) = 4 + 2 = 6 \) → \( (4, 6) \)
• When \( x = 5 \), \( f(5) = 5 + 2 = 7 \) → \( (5, 7) \)

The corresponding ordered pairs for the inverse function \( f^{-1}(x) = x - 2 \) will be:

• \( (1, -1) \)
• \( (2, 0) \)
• \( (3, 1) \)
• \( (4, 2) \)
• \( (5, 3) \)
• \( (6, 4) \)
• \( (7, 5) \)

Thus, looking at the provided choices, we need to find the set that represents pairs of the form \( (y, x - 2) \) or \( (y + 2, y) \).

However, the ordered pairs provided do not match exactly what we derived, unless we check their values. Upon inspection, it seems the correct pairs corresponding to the inverse are:

• \( (-1, -3) \) reflects that when \( f^{-1}(-3) = -1 \)
• \( (0, -2) \) reflects that when \( f^{-1}(-2) = 0 \)
• \( (1, -1) \)
• \( (2, 0) \)
• \( (3, 1) \)
• \( (4, 2) \)
• \( (5, 3) \)

Of the provided options, it matches the first response where:

\[ {(-1,-3),(0,-2),(1,-1),(2,0),(3,1),(4,2),(5,3)} \]

This describes the inverse function accurately.