# How do you find the intercepts, asymptotes and graph f(x)= 4^(x+1)-5?

Dec 10, 2017

See the following :)

#### Explanation:

When $x = 0$, $y = f \left(0\right) = {4}^{0 + 1} - 5 = {4}^{1} - 5 = 4 - 5 = - 1$
So, the y-intercept is $\left(0 , - 1\right)$.

When $y = 0$, which means $f \left(x\right) = 0$
${4}^{x + 1} - 5 = 0$
${4}^{x + 1} = 5$

take log on both sides:
$\log {4}^{x + 1} = \log 5$
$\left(x + 1\right) \log 4 = \log 5$
$x \log 4 + \log 4 = \log 5$
$x = \frac{\log 5 - \log 4}{\log} 4 = 0.160964047$
Therefore, x-intercept is $\left(0.16 , 0\right)$.

graph{4^(x+1)-5 [-18.48, 18.47, -9.24, 9.24]}