Given the function f(x)=3^x-1+2, find the y-intercept and express in coordinate point form.

Question

A. (0,-1)

B. (0,7/3)

C. (0,5)

D. (0,3)

E. None of the above

Answer 1

f(x) = 3^x-1 + 2

 

The y-intercept occurs where x = 0.  So let's set x = 0:

 

f(x) = 3^x-1 + 2

f(x=0) = 3^0-1 + 2

f(0) = 3^-1 + 2

f(0) = 1/3 + 2

f(0) = 1/3 + 6/3

f(0) = 7/3

 

So the coordinate is x = 0, y = 7/3, or (0,7/3)