Which graph represents an odd function?Answer by using: A, B, C, or D for each graph.
2 answers:
Answer: Option C is the correct graph.
Explanation:
An odd function satisfies the condition,
This indicates that for any point (x,y) on the graph, the point (-x,-y) will also be present.
Why Option C is correct:
Option C includes the point (1,2), which implies the point (-1,-2) must be present.
Indeed, (-1,-2) is among the points.
Other pairs like (2,3) with (-2,-3), (3,-1) with (-3,1), and (4,0) with (-4,0) are also found. Hence, the function represented is odd.
Why other options are incorrect:
In Option A, (1,3) is given, so at x = -1, y should be -3, but instead y = 1, so it’s not odd.
Option B has (1,0), so at x = -1, y should be 0, but y = -3, so it is not odd.
Option D features (1,-1), meaning at x = -1 y should be 1; however, y = -1, so it's not odd.
The graph displayed in the third position corresponds to an odd function. Choice (C) is correct.
Additional details:
An inverse function reverses the input-output pairs of another function: for f giving y from x, the inverse provides x from y.
The relation links inputs (domain) with outputs (range).
Definition: A function is odd if
If the points meet and
,
Then the points in graph (C): and
have pairs of the form
and
. This confirms the graph depicts an odd function.
Therefore, the third graph corresponds to an odd function. Option (C) is correct.
Learn more:
- Explore inverse functions at brainly.com/question/1632445.
- Study circle equations at brainly.com/question/1506955.
- Understand domain and range at brainly.com/question/3412497.
Details:
Grade: High School
Subject: Mathematics
Topic: Ratio and Proportion
Keywords: proportion, direct proportionality, constant, proportionality equation, y=0.41x, constant of proportionality.
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