# How do you graph y=-3*2^(x+2)?

Jul 20, 2017

$y$ has the standard graph of ${2}^{x}$ scaled by $- 12$

#### Explanation:

$y = - 3 \cdot {2}^{x + 2}$

Since ${2}^{x + 2} > 0 \forall x \in \mathbb{R} \to y < 0 \forall x \in \mathbb{R}$

In other words, $y$ is always negative.

Now let's consider some other criteria of $y$

${\lim}_{x \to - \infty} y = 0$

${\lim}_{x \to + \infty} y = - \infty$

$y \left(0\right) = - 3 \cdot {2}^{2} = - 12$

$y = - 3 \times {2}^{2} \cdot {2}^{x} = - 12 \cdot {2}^{x}$

$y$ has the standard graph of ${2}^{x}$ scaled by $- 12$

The graph of $y$ is shown below.

graph{-3*2^(x+2) [-36.3, 36.8, -29.95, 6.53]}