Which graph represents an odd function? answer by using: a, b, c, or d for each graph.

The correct option is C.

Explanation:

A function is called an odd function if,

It means if the points are in the form of (x,y) then (-x,-y) is also in the graph.

Reason for correct option:

In option C, a point  (1,2),

It means,

And we have another point (-1,-2).

The other points are (2,3),(-2,-3),(3,-1),(-3,1),(4,0),(-4,0). Therefore the function is an odd function.

Reason for incorrect option:

In option A, a point is (1,3), therefore the value of function at x = -1 should be -3.

But the value of function is 1 at x=-1, therefore it is not an odd function.

In option B, a point is  (1,0), therefore the value of function at x = -1 should be 0.

But the value of function is -3 at x=-1, therefore it is not an odd function.

In option D, a point is (1,-1), therefore the value of function at x = -1 should be 1.

But the value of function is -1 at x=-1, therefore it is not an odd function.

The third graph is an odd function. Option (C) is correct.

Further explanation:

A function that is a reverse of another function is known as an inverse function. If we substitute x in a function f and it gives a result of y then its inverse z to y gives the result x.

The relation is defined as the relationship between the input values and output values.

The x coordinates are the domain of the function and the y coordinates are the range of the function.

Explanation:

An odd function can be defined as if

If the points of the function are as and

The points that are in the graph (C) are and

All the points are in the form of and . Therefore, the graph is an odd function.

The third graph is an odd function. Option (C) is correct.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Ratio and proportion

Keywords: proportional, directly proportional, constant, proportionality equation, y=0.41x, constant of proportionality.