SOLUTION: 1. For the functions f(x) = 2^x and g(x) = 3^x : a) What are the Domains and Ranges of these functions? b) What point(s) do they have in common and why? c) Starting with y

Algebra ->  Rational-functions -> SOLUTION: 1. For the functions f(x) = 2^x and g(x) = 3^x : a) What are the Domains and Ranges of these functions? b) What point(s) do they have in common and why? c) Starting with y      Log On


   

Question 1194666: 1. For the functions f(x) = 2^x and g(x) = 3^x :
a) What are the Domains and Ranges of these functions?
b) What point(s) do they have in common and why?
c) Starting with y = 2^x, what would y = 2^x+4 - 3 look like in comparison to y = 2^x?
d) How does y=(1/2)^x look in relation to y = 2^x? Why is this?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

1. For the functions
f%28x%29+=+2%5Ex+and
g%28x%29+=+3%5Ex++

a) What are the Domains and Ranges of these functions?
for f%28x%29+=+2%5Ex+:
domain :+R (all real numbers)
range: { f%28x%29 element R+: f%28x%29+%3E+0 } (all positive real numbers)
for g%28x%29+=+3%5Ex++:
domain :+R (all real numbers)
range: { g%28x%29 element R+: g%28x%29+%3E+0 } (all positive real numbers)

b) What point(s) do they have in common and why?

points where f%28x%29+=+g%28x%29+
2%5Ex=+3%5Ex+ ........ since the bases are different, equation will be true only if x=0
2%5E0=+3%5E0
1=1


c) Starting with y+=+2%5Ex, what would y+=+2%5E%28x%2B4%29+-+3 look like in comparison to y+=+2%5Ex?
Parent Function: y+=+2%5Ex
Horizontal Shift: Left ,4 units
Vertical Shift: Down , 3 units
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2%5Ex%2C+2%5E%28x%2B4%29-3%29+

d) How does y=%281%2F2%29%5Ex look in relation to y+=+2%5Ex? Why is this?
these are inverse to each other
since %281%2F2%29%5Ex+=1%2F2%5Ex -> which is inverse to 2%5Ex

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2%5Ex%2C+%281%2F2%29%5Ex%29+