Question

What are the domain and range of the absolute value parent function?

Answer 1

The domain : All real numbers

The range : From 0 to positive infinity

Explanation:

The absolute value function is f(x) = lxl where the bars around the x mean take whatever x value and make it positive. So

f(3) = l3l = 3

f(7) = l7l = 7

f(-7) = l-7l = 7

So this function can take any real number from negative infinity to positive infinity.

Since the function makes all inputs positive, then all positive inputs will come out positive, all negative inputs will be made positive (as per my example above) and zero will remain 0. So the range (set of output values) starts from zero and goes to positive infinity

Answer 2

The domain is all real numbers and the range is all positive numbers.

The absolute parent function is f(x)=|x|.

The domain, or values of x, can be any real number. There is no x that will not give an answer in this function.

The range, or values of y, must be negative numbers. This is because the absolute value function makes values positive, since they are distance from 0.