# How do you find the intercepts, asymptotes and graph y = 2^(x/4)?

May 18, 2018

See explanantion

#### Explanation:

When $x = 0$ we have ${2}^{0} = 1$

When $0 < x < 4$ then $0 < {2}^{\frac{x}{4}} < 1$

When $x < 0$ then we have $0 < \frac{1}{{2}^{| \frac{x}{4} |}} < 1$

When $x > 4$ then we have ${2}^{\frac{x}{4}} > 1$

Negative infinity $\to {\lim}_{x \to {\infty}^{-}} {2}^{\frac{x}{4}} \to k = 0$

Positive infinity $\to {\lim}_{x \to {\infty}^{+}} {2}^{\frac{x}{4}} \to k = {\infty}^{+}$