Question

DO NOT GIVE ANSWER! I just need an explanation.

Answer 1

Hi there!

The range of a function describes its possible y-values. For example, y=x produces a linear graph. Its range is all real numbers, meaning that for any value of y, the function is defined.

However, for y=x², for example, the range is y>0, since there the graph doesn't travel to y-values less than 0. The function is only defined when y>0.

To find the range of the given functions, you can try graphing them. Or, if you've memorized the ranges of their parent functions, you can try to take that and apply transformations.

Answer for the first question:

f(x)=-√x

The parent function is f(x)=√x. The range of this is y≥0.

f(x)=-√x

Adding a negative in front of the square root reflects the function across the x-axis, meaning the range is therefore flipped too:

y≤0

I hope this helps!