Question

What is the range of the function y = |x|?
x ≥ 0
y ≥ 0
all real numbers

Answer 1

well since any value you give x becomes positive (because you take absolute value of x and absolute value is always positive) the resulting y value must be always greater than equal to 0 for real numbers. every value you gives to x gives a corresponding positive or 0 y value like in the examples: y=|0| -> y=0 y=|-4| -> y=4

y value is always 0 or more -> y ≥ 0

Answer 2

to be specific range is always the possible values y can get and in this case it can get 0 or more. The domain of a function is the possible values x can have, and in this case it's all real numbers. that is why the range is all positive real numbers so numbers ≥ 0