SOLUTION: Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Transform the second expression into the equivalent logarithmic equation;

Algebra ->  Graphs -> SOLUTION: Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Transform the second expression into the equivalent logarithmic equation;       Log On


   

Question 211246: Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Transform the second expression into the equivalent logarithmic equation; and evaluate the logarithmic equation for three values of x that are greater than 1, three values of x that are between 0 and 1, and at x=1. Use the resulting ordered pairs to plot the graph of each function.
So for this problem there will be two lines on one graph? How do I plot the points? I'm really lost on this one and any help would be appreciated. I'd also be willing to pay a tutor for help on this! Please contact me if interested! Thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Well it helps to have the entire problem. What is the given function?


If you're having problems graphing in general, here's an example:


Problem: Graph y=2%5Ex


Solution:



In order to graph y=2%5Ex, we need to plot a few points.


To get points in the form of (x,y), we need to find corresponding 'y' values to given 'x' values.


Let's find the y value when x=-2 note: you can start at any x value.


y=2%5Ex Start with the given equation.


y=2%5E%28-2%29 Plug in x=-2.


y=0.25 Evaluate 2%5E%28-2%29 to get 0.25


So if x=-2, then y=0.25 which gives us the point (-2,0.25).


----------------------------


Let's find the y value when x=-1.5


y=2%5Ex Start with the given equation.


y=2%5E%28-1.5%29 Plug in x=-1.5.


y=0.354 Evaluate 2%5E%28-1.5%29 to get 0.354


So if x=-1.5, then y=0.354 which gives us the point (-1.5,0.354).


----------------------------


Let's find the y value when x=-1


y=2%5Ex Start with the given equation.


y=2%5E%28-1%29 Plug in x=-1.


y=0.5 Evaluate 2%5E%28-1%29 to get 0.5


So if x=-1, then y=0.5 which gives us the point (-1,0.5).


----------------------------


Let's find the y value when x=-0.5


y=2%5Ex Start with the given equation.


y=2%5E%28-0.5%29 Plug in x=-0.5.


y=0.707 Evaluate 2%5E%28-0.5%29 to get 0.707


So if x=-0.5, then y=0.707 which gives us the point (-0.5,0.707).


----------------------------


Let's find the y value when x=0.5


y=2%5Ex Start with the given equation.


y=2%5E%280.5%29 Plug in x=0.5.


y=1.414 Evaluate 2%5E%280.5%29 to get 1.414


So if x=0.5, then y=1.414 which gives us the point (0.5,1.414).


----------------------------


Let's find the y value when x=1


y=2%5Ex Start with the given equation.


y=2%5E%281%29 Plug in x=1.


y=2 Evaluate 2%5E%281%29 to get 2


So if x=1, then y=2 which gives us the point (1,2).


----------------------------


Let's find the y value when x=1.5


y=2%5Ex Start with the given equation.


y=2%5E%281.5%29 Plug in x=1.5.


y=2.828 Evaluate 2%5E%281.5%29 to get 2.828


So if x=1.5, then y=2.828 which gives us the point (1.5,2.828).


----------------------------


Let's find the y value when x=2


y=2%5Ex Start with the given equation.


y=2%5E%282%29 Plug in x=2.


y=4 Evaluate 2%5E%282%29 to get 4


So if x=2, then y=4 which gives us the point (2,4).


----------------------------


Let's find the y value when x=2.5


y=2%5Ex Start with the given equation.


y=2%5E%282.5%29 Plug in x=2.5.


y=5.657 Evaluate 2%5E%282.5%29 to get 5.657


So if x=2.5, then y=5.657 which gives us the point (2.5,5.657).


----------------------------


Let's find the y value when x=3


y=2%5Ex Start with the given equation.


y=2%5E%283%29 Plug in x=3.


y=8 Evaluate 2%5E%283%29 to get 8


So if x=3, then y=8 which gives us the point (3,8).


----------------------------


Now let's make a table of the values we just found.


Table of Values:





xy
-20.25


-1.50.354


-10.5


-0.50.707


0.51.414


12


1.52.828


24


2.55.657


38

Now let's plot the points:




Graph:


Now draw a curve through all of the points to graph y=2%5Ex:


Graph of y=2%5Ex