Question

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

Answer 1

See the following :)

Explanation:

When `x=0`, `y=f(0)=4^(0+1)-5=4^1-5=4-5=-1`
So, the y-intercept is `(0,-1)`.

When `y=0`, which means `f(x)=0`
`4^(x+1)-5=0`
`4^(x+1)=5`

take log on both sides:
`log4^(x+1)=log5`
`(x+1)log4=log5`
`xlog4+log4=log5`
`x=(log5-log4)/log4=0.160964047`
Therefore, x-intercept is `(0.16, 0)`.

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