# How do you graph the exponential function f(x) = 3^x+1?

Aug 24, 2016

$f \left(x\right) > 1$ for all $x \in \mathbb{R}$; $f \left(0\right) = 2$; ${\lim}_{\text{x-> -oo}} f \left(x\right) = 1$
See graph below

#### Explanation:

$f \left(x\right) = {3}^{x} + 1$

Since ${3}^{x} > 0$ for all $x \in \mathbb{R}$
$f \left(x\right) > 1$ for all $x \in \mathbb{R}$

$f \left(0\right) = {3}^{0} + 1 = 1 + 1 = 2$

${\lim}_{\text{x-> -oo}} f \left(x\right) = 0 + 1 = 1$

graph{3^x+1 [-10, 10, -5, 5]}