Question

What is the range of f(x) = 3^x + 9?

{y | y < 9}
{y | y > 9}
{y | y > 3}
{y | y < 3}

I don't understand what range is besides the y values, but I don't understand how to find it either. Can someone help me out?

Answer 1

Would it be y>9?

Answer 2

The range in this context would seem to mean the possible values the function can output.

Answer 3

First, let's consider the range of \(3^x\). It's a one-to-one increasing function, so his minima and maxima will be at the ends of its domain, which we'll assume is \((-\infty, \infty)\).
Analyzing these points shows that its range is going to be \((0,\infty)\).

If we are to add \(9\) to our function, it will just shift our range up, giving us \((9,\infty)\).
This interval can be expressed alternatively as \(\{y\ |\ y>9\}\).