Question

The asymptote of the function f(x) = 3^x+1 - 2 is ____. Its y-intercept is ____.

Blank 1: A. y = -2
B. y = -1
C. y = 1
D. y = 2

Blank 2: A. (0,2)
B. (0,-3)
C. (0,1)
D. (0,-1)

Answer 1

we are given the function f(x) = 3^x+1 - 2 and is asked for the asymptote and y-intercept. In this case, we transform the function to

y +2 = 1/3^(x+1)-1
y = 1-2/3^(x+1)-1/(3^(x+1)-1)
let 3^(x+1)-1 = 0
1/3^(x+1) = 0
x = infinity
when x = infinity
y = 0 - 2
y = -2

The y-intercept is the value where x = 0. substituting,

y = 3^(0+1) - 2 = 1