Question

Which of the following equations is NOT an example of inverse

variation?
1. f(x) = kx
11. f(x) = 2k/x
III. f(x) =-kx/z

Answer 1

i and iii are not examples of inverse variation.

Explanation:

Inverse variation between two variables, y and x, is written as:

y = k/x

This means that, as the absolute value of x increases, the absolute value of y decreases.

So we need to have the variable in the denominator.

Let's analyze the given options:

i) f(x) = k*x

Here, x is not in the denominator, this is a direct variation, so this is not an example of inverse variation.

ii) f(x) = 2k/x

Here we can see that the variable x is in the denominator, thus, this is an inverse variation.

iii) f(x) = -k*x/z

We can see that we have z in the denominator, but you can see that the variable is x, and x is in the numerator, thus, this is not an example of inverse variation.

We can conclude that:

f(x) = kx

and

f(x) =-kx/z

Are not examples of inverse variation.