Question

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

Answer 1

Answer: The correct option is C.

Explanation:

A function is called an odd function if,

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

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,

$f(1)=2$

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

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

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.

Answer 2

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

If the points of the function are as $\left( {x,y} \right)$ and $\left( {- x,- y} \right).$

The points that are in the graph (C) are $\left( {2,3} \right), \left( {-2,-3} \right), \left( {3, - 1} \right), \left( { - 3,1} \right), \left( {4,0} \right), \left( { - 4,0} \right)$ and $\left( {1,2} \right).$

All the points are in the form of $\left( {x,y} \right)$ and $\left( {- x,- y} \right)$. Therefore, the graph is an odd function.

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

Learn more:

1. Learn more about inverse of the function brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Ratio and proportion

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