Click on this link for a file that has Mapping Diagram blanks (2 and 3 axes) for use in the following exercises.
1. For each  positive power function complete the function table and then create the corresponding mapping diagram and locate the "extreme point" if one exists.

a.
 $x$ $f(x)=2x^3$ 2 1 0 -1 -2

b.
 $x$ $f(x)= -2x^3$ 2 1 0 -1 -2

c.
 $x$ $f(x)= -(x+1)^4 + 1$ 2 1 0 -1 -2
d.
 $x$ $f(x)= (x-1)^4-1$ 2 1 0 -1 -2
2. For each negative power function complete the function table and then create the corresponding mapping diagram and locate the "pole" .

a.
 $x$ $f(x)= x^{-2}$ 2 1 0 -1 -2

b.
 $x$ $f(x)=-x^{-3}$ 2 1 0 -1 -2

c.
 $x$ $f(x)= (x+1)^{-2} -1$ 2 1 0 -1 -2
d.
 $x$ $f(x)=(x-1)^{-3}+1$ 2 1 0 -1 -2
3. For the  functions in problem 1 and 1 d,  find any values of $a$ where $f(a) = 0$.
4. For the functions in problem 2 and 2 d,  find any values of $a$ where $f(a) = 0$.
5. Suppose $f$ is a polynomial function of degree 4 with $f(x)=A(x-2)^2 (x-1)(x+1)$  and $f(0) = 6. a. Determine$A$and the roots of$f$. b. Find$f(-2)$and$f(3)$. c. Give the standard polynomial function form for$f$. d. Exhibit the results of your work on a graph and a mapping diagram. 6. Suppose$f$is a linear fractional rational function with$f(x)= \frac {2x-a} {x-b}$with its pole at$x=1$with$f(0)= 3$. a. Determine$a$and$b$. b. Use the values of$a$and$b$to find$f(-1)$and$f(2)$. c. Give the polynomial - proper rational function form for$f$based on the given information. d. Solve the equation$f(x) = 0$and display the solutions on your mapping diagram. 7. For each of the following cubic polynomial functions, create a mapping diagram for the function treated as a composition of core linear functions and the core power function$P_3(x)=x^3$. a.$f(x)=2x^3 + 1$b.$f(x)= -2(x-1)^3 - 3$c.$f(x)=\frac 1 2 x^3 + \frac 1 2$d.$f(x)=-\frac 1 2 (x+1)^3 + \frac 1 2$8. For each of the following rational functions create a mapping diagram for the function treated as a composition of core linear functions and the core power function$P_3^{-1}(x)=\frac 1 {x^3} = x^{-3}$. a.$f(x)=2x^{-3} + 1$b.$f(x)= -2(x-1)^{-3} - 3$c.$f(x)=\frac 1 {2 x^3}+ \frac 1 2$d.$f(x)=-\frac 1 {2 (x+1)^3} + \frac 1 2$9. For each of the following functions use "socks and shoes" to find and create a mapping diagram for its inverse function for the domain$(-\infty,\infty)$. a.$f(x)=2x^3 + 1$b.$f(x)= -2(x-1)^3 - 3$c.$f(x)=\frac 1 {2 x^3}+ \frac 1 2$d.$f(x)=-\frac 1 {2 (x+1)^3} + \frac 1 2\$