Question

A cross section of a parabolic glass mirror of the Hubble space telescope shown can be modeled by the graph of the function y=0.0043x^2 where x and y are measured in meters. Find the domain and range of the function in this situation

Answer 1

Hello there!

Let's take a look at the function
y=0.0043x²

The domain is all real numbers because there are no variables in the denominator or under a radical!
domain: (-∞,∞)

Now for the range, let's find the inverse function.
Switch x and y...
x=0.0043y²
Now solve for y...
x/0.0043=y²
sqrt(0.0043/x)=y

Now because the denominator CANNOT multiply to 0, set the denominator equal to 0 to see what x CAN'T be. This means that x cannot be 0 so the range is all reals besides 0.
Range: (-∞,0)U(0,∞)

I really hope this helps!
Best wishes :)

NOTE: if you need an explanation as to WHY though find the inverse function's domain to get the Original function's range, feel free to message me!