SOLUTION: Find the range and horizontal asymptote of the exponential function y = 3^x - 1. a. Range: (-1, inf) Horizontal asymptote: y = -1 b. Range: (0, inf) Horizontal asym

Algebra ->  Functions -> SOLUTION: Find the range and horizontal asymptote of the exponential function y = 3^x - 1. a. Range: (-1, inf) Horizontal asymptote: y = -1 b. Range: (0, inf) Horizontal asym      Log On


   

Question 43185: Find the range and horizontal asymptote of the exponential function y = 3^x - 1.
a. Range: (-1, inf)
Horizontal asymptote: y = -1

b. Range: (0, inf)
Horizontal asymptote: y = 0

c. Range: [0, inf)
Horizontal asymptote: y = 0

d. Range: All real numbers
Horizontal asymptote: None

e. None of the others

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+3%5Ex+-+1
Think about this:
y+=+3%5Ex
Three to any power is always greater than zero: y+%3E+0
Asymptote: y+=+0
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3%5Ex%2C+0%29+
Now, think about this:
y+=+3%5Ex+-+1
Same concept, but every unit is one less: y+%3E+-1
Asymptote: y+=+-1
Range: y+%3E+-1 (-1,+infinity)
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3%5Ex+-+1%2C+-1%29+
It is (A).