Question

How to find the range of the function R(z) = 5/(z^3+20z^2+9z) ?

Answer 1

Hmm... I'm guessing this is from your precalc class?

Answer 2

If you need to do it algebraically, that seems difficult... but you can do it analytically to find the range.

Answer 3

First note that y can never be zero - since the numerator is 5, and nothing you divide 5 by will make it equal to zero.

And when the denominator is near zero but positive (like positive 0.0001 for example) the function approaches positive infinity (5 divided by a very small positive number)

When the denominator is near zero but negative ( -0.0001 for example) the function approaches negative infinity (5 divided by a very small negative number).

The only restriction on the range is that y cannot equal zero.