# How do you find the range of a function?

A function means a correspondence from one value x of the first set to another value y of the second set.

## Answer: To find the range of the function [y = f(x)] we solve the function for x.

Range** **is all the values that come out as output of the function involved.

**Explanation:**

The range of a function is the set of all its outputs.

Let's say a function f(x)

The spread of all values of f(x) from minimum to the maximum is the range for the function

In the given expression of y, substitute all the values of x to check whether it is positive, negative, or equal to other values. Find the minimum and maximum values for y.

For example find the range of y = x / (3 - x)

Lets solve the equation for x

So, 3y - xy = x

x + xy = 3y

x = 3y / (1 + y)

The final equation is a fraction and a fraction is NOT defined when its denominator is zero. Thus

1 + y ≠ 0

y ≠ -1

Therefore, {y ∈ R | y ≠ -1} or y ∈ (−∞,−1) ∪ (-1,∞)