Exponential FunctionsWe are interested in the graphs of NiMvLSUiZkc2IyUieEcpJSJhR0Yn, where a >1. Example 1: If NiMvLSUiZkc2IyUieEcpIiIjRic=. Then (1) plot f; (2) what is f(0); (3) what happens to f when x gets large (NiMlKWluZmluaXR5Rw==) ? (4) what happens to f when x gets small (NiMsJCUpaW5maW5pdHlHISIi)?f:=x->2^x;

NiM+JSJmR2YqNiMlInhHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0dGKCkiIiM5JEYoRihGKA==

plot(f,-5..5,-1..10);

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

f(100);

NiMiQHdgPy5uXCwlSCNHLWddd0Ui

evalf(f(-100));

NiMkIitfITQnKSl5ISNT

Exercise 1: Answer the questions listed in "Example 1" by using the function NiMvLSUiZkc2IyUieEcpIiM1Ric=.Example 2: Use the shifting/reflection techniques to graph the each of the following functions together with NiMvLSUiZkc2IyUieEcpIiIjRic=.[Do them by hands first and verify your answers with Maple].(1) NiMvLSUjZjFHNiMlInhHLCYpIiIjRiciIiJGKkYr (2) NiMvLSUjZjJHNiMlInhHLCYpIiIjRiciIiJGKiEiIg==(3) NiMvLSUjZjNHNiMlInhHKSIiIywmRiciIiJGKSEiIg==(4) NiMvLSUjZjRHNiMlInhHKSIiIywmRiciIiJGKUYr(5) NiMvLSUjZjVHNiMlInhHKSIiIywkRichIiI=(6) NiMvLSUjZjZHNiMlInhHLCQpIiIjRichIiI=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;

NiM+JSNmMUdmKjYjJSJ4RzYiNiQlKW9wZXJhdG9yRyUmYXJyb3dHRigsJikiIiM5JCIiIkYuRjBGKEYoRig=NiM+JSNmMkdmKjYjJSJ4RzYiNiQlKW9wZXJhdG9yRyUmYXJyb3dHRigsJikiIiM5JCIiIiEiI0YwRihGKEYoNiM+JSNmM0dmKjYjJSJ4RzYiNiQlKW9wZXJhdG9yRyUmYXJyb3dHRigpIiIjLCY5JCIiIiEiI0YwRihGKEYoNiM+JSNmNEdmKjYjJSJ4RzYiNiQlKW9wZXJhdG9yRyUmYXJyb3dHRigpIiIjLCY5JCIiIkYtRjBGKEYoRig=NiM+JSNmNUdmKjYjJSJ4RzYiNiQlKW9wZXJhdG9yRyUmYXJyb3dHRigpIiIjLCQ5JCEiIkYoRihGKA==NiM+JSNmNkdmKjYjJSJ4RzYiNiQlKW9wZXJhdG9yRyUmYXJyb3dHRigsJCkiIiM5JCEiIkYoRihGKA==

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);

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

Exercise 3. Given that NiMvLSUiZkc2IyUieEcsJikiIiRGJyIiIiIiI0Yr.(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 NiMvLSUiZkc2IyUieEcsJikiIiQsJEYnISIiIiIiIiIlRi0=. (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.