Answer: The correct option is C.
Explanation:
A function is called an odd function if,
[tex]f(-x)=-f(x)[/tex]
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,
[tex]f(1)=2[/tex]
And we have another point (-1,-2).
[tex]f(-1)=-f(1)=-2[/tex]
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 [tex]f\left( { - x} \right) = - f\left( x \right).[/tex]
If the points of the function are as [tex]\left( {x,y} \right)[/tex] and [tex]\left( {- x,- y} \right).[/tex]
The points that are in the graph (C) are [tex]\left( {2,3} \right), \left( {-2,-3} \right), \left( {3, - 1} \right), \left( { - 3,1} \right), \left( {4,0} \right), \left( { - 4,0} \right)[/tex] and [tex]\left( {1,2} \right).[/tex]
All the points are in the form of [tex]\left( {x,y} \right)[/tex] and [tex]\left( {- x,- y} \right)[/tex]. 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.
