Finding Intercepts, Zeros, and Asymptotes of f(x) = 4^(x+2)

Published on September 8, 2026

Functions

Learn how to find the x-intercept, y-intercept, zeros, and horizontal asymptote for the exponential function f(x) = 4^(x+2) step-by-step.

Question

Given f ( x ) = 4 x + 2 f(x)=4 x+2 Find the following ⁣ : : (a) x x-intercept and y y-intercept x x-intercept ⁣ : ( 16 , 0 ) :(16,0) and y y-intercept ⁣ : ( 0 , 16 ) :(0,16) x x-intercept ⁣ : ( 4 , 0 ) :(4,0) and no y y-intercept x x-intercept ⁣ : ( 4 , 0 ) :(4,0) and y y-intercept ⁣ : ( 0 , 16 ) :(0,16) No x x-intercept and y y-intercept ⁣ : ( 0 , 16 ) :(0,16) (b) Zero/s 16 16 8 8 4 4 No zero (c) Asymptotes y = 4 y=4 y = 0 y=0 y = − 4 y=−4 No horizontal asymptote

Answer

Given

(a) -intercept and -intercept

To find the -intercept, set :

Since an exponential function of the form (where ) is always positive, there is no -intercept.
To find the -intercept, set :

The -intercept is .