Exponential Functions
We are interested in the graphs of , where a >1.
Example 1: If . Then
(1) plot f;
(2) what is f(0);
(3) what happens to f when x gets large ( ) ?
(4) what happens to f when x gets small ( )?
> | f:=x->2^x; |
> | plot(f,-5..5,-1..10); |
> | f(100); |
> | evalf(f(-100)); |
Exercise 1: Answer the questions listed in "Example 1" by using the function .
Example 2: Use the shifting/reflection techniques to graph the each of the following functions together with .[Do them by hands first and verify your answers with Maple].
(1)
(2)
(3)
(4)
(5)
(6)
> | f1:=x->2^x+2;f2:=x->2^x-2;f3:=x->2^(x-2);f4:=x->2^(x+2);f5:=x->2^(-x);f6:=x->-2^x; |
Note. The following Maple syntax is to plot two functions together. [1] Do you see that f1 is a vertical shifting of f? [2] What about f2, f3, f4, f5, f6 in relation to f?
> | plot({f,f1},-3..6,-1..10,thickness=2); |
Exercise 3. Given that .
(a) Find g that is being horizontally shifted to the right 3 units from f.
(b) Find h that is being vertically shifted down 5 units from g.
Note: You should be able to do this by hand first and verify your answer with Maple or ClassPad.
Exercise 4: Given that .
(a) Find g that is being horizontally shifted to the right 3 units from f.
(b) Find h that is being vertically shifted down 5 units from g.
Note: You should be able to do this by hand first and verify your answer with Maple or ClassPad.