Question
If the point \( (7,43) \) is on the graph of \( f(x) \), what point must be on the graph of \( -f(-x) \) ? (1 point) \( (-7,43) \) \( (7,43) \) \( (-7,-43) \) \( (7,-43) \)
Ask by Clark Barnett. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The point \( (-7, -43) \) must be on the graph of \( -f(-x) \).
Solution
The original point is \( (7, 43) \), which means \( f(7) = 43 \).
To find a point on the graph of \( -f(-x) \):
1. Let \( g(x) = -f(-x) \).
2. We need to find \( g(a) \) such that \( g(a) = -f(-a) \).
Given \( f(7) = 43 \), set \( -a = 7 \) which gives \( a = -7 \).
Thus:
\[
g(-7) = -f(-(-7)) = -f(7) = -43
\]
So, the corresponding point on the graph of \( -f(-x) \) is \( (-7, -43) \).
**Answer:** \( (-7,-43) \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To find the corresponding point on the graph of \( -f(-x) \) given that the point \( (7,43) \) is on \( f(x) \), we first look at the transformations involved. The point \( (7, 43) \) means that \( f(7) = 43 \). Now, consider \( -f(-x) \): 1. The transformation \( -x \) will reflect the point across the y-axis. So, we replace \( x \) with \( -7 \), leading to the point \( (-7, f(7)) \). 2. Then we apply the negative transformation, which takes the y-coordinate and flips its sign, resulting in \( (-7, -43) \). So, the point that must be on the graph of \( -f(-x) \) is \( (-7, -43) \).
