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1 month ago

Which graph represents an odd function?Answer by using: A, B, C, or D for each graph.

Mathematics

2 answers:

AnnZ [12.3K]1 month ago

6 0

Answer: Option C is the correct graph.

Explanation:

An odd function satisfies the condition,

$f(-x)=-f(x)$

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.

$f(1)=2$

Indeed, (-1,-2) is among the points.

$f(-1)=-f(1)=-2$

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.

AnnZ [12.3K]1 month ago

3 0

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 $f\left( { - x} \right) = - f\left( x \right).$

If the points meet $\left( {x,y} \right)$ and $\left( {- x,- y} \right).$ ,

Then the points in graph (C): $\left( {2,3} \right), \left( {-2,-3} \right), \left( {3, - 1} \right), \left( { - 3,1} \right), \left( {4,0} \right), \left( { - 4,0} \right)$ and $\left( {1,2} \right).$ have pairs of the form $\left( {x,y} \right)$ and $\left( {- x,- y} \right)$ . 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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Step-by-step explanation:

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