How do you graph y=(1/3)^x+1?

Dec 29, 2017

See below.

Explanation:

First find common coordinates:

y axis intercept occurs when $x = 0$:

$y = {\left(\frac{1}{3}\right)}^{0} + 1 = 2 \textcolor{w h i t e}{88}$ coordinate $\left(0 , 2\right)$

x axis intercepts occur when $y = 0$:

${\left(\frac{1}{3}\right)}^{x} + 1 = 0$ ( no real number solutions to this )

No x axis intercepts.

as $x \to \infty$ , $\textcolor{w h i t e}{88} {\left(\frac{1}{3}\right)}^{x} + 1 \to 1$

as $x \to - \infty$ , $\textcolor{w h i t e}{88} {\left(\frac{1}{3}\right)}^{x} + 1 \to \infty$

The line $y = 1$ is a horizontal asymptote.

GRAPH: