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.

Learn more:

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Ratio and proportion

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

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer