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

Nov 13, 2016

graph{y=8 2^x [-10, 10, -5, 5]}

#### Explanation:

Here, $y = {2}^{x + 3} = {2}^{x} {2}^{3} = 8 \left({2}^{x}\right)$, an exponential function.

As $x \to - \infty , y \to 0$. So, negative x-axis is the asymptote.

The graph cuts y-axis at (0, 8). The y-growth is exponential. In other

words, y-growth is fast for greater x.

A short Table for making the graph:

#(x, y): ...(-4, 1/2) (-3, 1) (-2, 2) (-1, 4) (0, 8) (1, 16) (2, 32) (3, 64) (4, 128)..

For information, as Y= log y = x log 2 + log 8, on a semi-log graph,

the graph of Y vs x will be a stright line, with slope Y'=2 and Y-

intercept 8.