SOLUTION: a. Describe the transformation that have been applied to the graph of F(x)=2^x to obtain the graph f(x)2^(x+1)-3 b. what is the Domain & Range of f(x)=2^(x+1)-3? c. What is

Algebra ->  Graphs -> SOLUTION: a. Describe the transformation that have been applied to the graph of F(x)=2^x to obtain the graph f(x)2^(x+1)-3 b. what is the Domain & Range of f(x)=2^(x+1)-3? c. What is      Log On


   

Question 1129864: a. Describe the transformation that have been applied to the graph of F(x)=2^x to obtain the graph f(x)2^(x+1)-3
b. what is the Domain & Range of f(x)=2^(x+1)-3?
c. What is the equation of the asymptote for the graph of f(x)=2^(x+1)-3?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

a.
to describe the transformation that have been applied to given exponential function, recall:
y=a%2Ab%5E%28x-h%29%2Bv where a is the vertical transformation, h is the horizontal shift, and v+is the vertical shift

if given the graph of F%28x%29=2%5Ex+ and obtain the graph f%28x%29=2%5E%28x%2B1%29-3
based on this equation, you see that
h+=+-1 and it means F%28x%29 has been shifted one+unit to the left+
and, v+=+-3 means F%28x%29+has been shifted three units down


b.
what is the Domain & Ranger of f%28x%29=2%5E%28x%2B1%29-3?
Domain: R (all real numbers)
Range: { f%28x%29 element R : f%28x%29+%3E+-3 }


c. what is the equation of the asymptote for the graph of f%28x%29=2%5E%28x%2B1%29-3?

lim%28x-%3E-infinity%29+%282%5E%28x+%2B+1%29+-+3%29+=+-3
Horizontal asymptote: y=-3

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2%5Ex%2C+2%5E%28x%2B1%29-3%2C-3%29+