# How do you graph y>2^x-4?

Dec 15, 2016

Plot $y = {2}^{x} - 4$ but with a dotted line.

The dotted line signifies that the value of y can never actually be ${2}^{x} - 4$

#### Explanation:

$\textcolor{b l u e}{\text{Determine the key points}}$

When x=0" "ul("the dotted line") goes through $y = 1 - 4 = - 3$

When y=0" "ul("the dotted line") goes through ${2}^{x} = 4 \implies x = 2$

As $x$ increases a lot ${2}^{x}$ increases a lot and the influence of -4 from $y > {2}^{x} - 4$ becomes less and less until it becomes isignificant.

$\text{ } {\lim}_{x \to + \infty} y > {\lim}_{x \to \infty} {2}^{x} \to \infty$

As $x$ decreases it becomes negative so we have

$y > {2}^{- x} - 4 \text{ "->" } y > \frac{1}{{2}^{+ x}} - 4$ giving:

$\text{ } {\lim}_{x \to - \infty} y > {\lim}_{x \to \infty} \frac{1}{{2}^{x}} - 4 \to - 4$