# How do you graph y=1.1(3)^x?

May 14, 2018

See explanation

#### Explanation:

Given: $1.1 {\left(3\right)}^{x}$

Just because I prefer it this way write as $y = \frac{11}{10} \times {3}^{x}$

color(blue)("Determine the "y_("intercept"))

The ${y}_{\text{intercept}}$ occurs at $x = 0$

However, ${3}^{0} = 1$ giving

$\textcolor{b r o w n}{{y}_{\text{intercept}} = \frac{11}{10} \times 1 = \frac{11}{10}}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Consider the case } x < 0}$

This changes ${3}^{x}$ into some root of $3$

So as $x$ becomes increasingly negative ${3}^{x}$ becomes less and less. So as $x$ tends to negative infinity then:

$\textcolor{b r o w n}{y = \frac{11}{10} \times {\lim}_{x \to {\infty}^{-}} \left({3}^{x}\right) \textcolor{w h i t e}{\text{ddd") ->color(white)("ddd}} y = \frac{11}{10} \times 0 = 0}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Consider the case } x > 0}$

As $x$ becomes increasingly greater the ${3}^{x}$ increases exponentially.

color(brown)(y=11/10xxlim_(x->oo^(+))(3^x)color(white)("ddd") ->color(white)("ddd") y=11/10xxoo = oo 