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

1 Answer
Dec 10, 2017

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]}