# How do you graph y=6(1/2)^(x+5)-2?

Dec 2, 2016

The exponential-decay Graph for $y = \frac{3}{16} {\left(\frac{1}{2}\right)}^{x} - 2$ is inserted.

#### Explanation:

$y = 6 {\left(\frac{1}{2}\right)}^{x + 5} - 2 = 6 {\left(\frac{1}{2}\right)}^{5} {\left(\frac{1}{2}\right)}^{x} - 2 = \frac{3}{16} {\left(\frac{1}{2}\right)}^{x} - 2$.

y-intercept ( x = 0 ) is $- \frac{29}{16} > - 2$.

As $x \to \infty , y \to 0 \mathmr{and}$ as $x \to - \infty , y \to \infty$.

$y = - 2$ is the ( horizontal ) asymptote.

In ${Q}_{4}$, note that the initial vertical space 3/16, in between the

curve and the asymptote, tends to 0, as $x \to \infty .$.

graph{y-3/16(1/2)^x+2=0 [-40, 40, -20, 20]}