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

Question 1194670: 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? Explain each step and show each interim equation which illustrates each step. You may attach a graph if you'd like.
d) How does y = (1/2)^x look in relation to y = 2^x? Why is this?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Both functions are monotonically increasing -- an increase in x means an increase in y.

a) A positive number raised to any real number power is valid expression; and it is always positive. So the domain of both functions is all real numbers, and the range of both functions is y>0.

b) Since both functions are monotonically increasing, they will intersect at only one point. Since any number to the 0 power is equal to 1, the single point of intersection is (0,1).

c) I will assume by "2^x+4-3" what you mean is "2^(x+4)-3" = . The "x+4" shifts the graph 4 units to the left; then the "-3" shifts it 3 units down.

Here is a graph:
y=2^x (red),
y=2^(x+4) (green) (red, shifted 4 to the left),
y=2^(x+4)-3 (blue) (green, shifted 3 down)

d)

That means the graph of y=(1/2)x is the reflection in the y axis of y=2^x.

Here is a graph:
y=2^x (red);
y=(1/2)^x=2^(-x) (green)

RELATED QUESTIONS
1. For the functions f(x) = 2^x and g(x) = 3^x : a) What are the Domains and Ranges of (answered by MathLover1)

2. For the functions f(x) = - x + 1, g(x) = 4x �4 a. Find the composite... (answered by lwsshak3)

We are working with domains, ranges and functions. Here is one problem I've already... (answered by jsmallt9)

whats the domains of the functions g(x)=square root of x^2-36 and... (answered by solver91311)

Given the functions and given domains, find the associated ranges. f(x) = 0, domain =... (answered by jim_thompson5910)

FOR THE INDICATED FUNCTIONS F AND G,FIND FUNCTIONS F0G AND G0F, FIND THE DOMAINS.... (answered by Theo)

for the indicated functions f and g, ﬁnd the functions f�g ,and g�f, and... (answered by srinivas.g)

given the functions f(x) = 1-3x^2 and g(x) = sqrtx-1, find the functions (f+g) , (f-g),... (answered by josgarithmetic)