Click on this link for a file that has Mapping Diagram blanks (2 and 3 axes) for use in the following exercises.
You may want to try this using a spreadsheet. You can download a spreadsheet template for functions defined as described in this section by clicking here.
1. For each function complete the function table and then create the corresponding mapping diagram and graph.
a. $f(x) = -x$ when $x \ge 0$ and $f(x) = x +1$ otherwise
 $x$ $f(x)$ 2 1 0 -1 -2

b.$f(x) = 2x$ when $x \ge 0$ and $f(x) = -2x +1$ otherwise
 $x$ $f(x)$ 2 1 0 -1 -2

c.$f(x) = x^2$ when $x \ge 0$ and $f(x) = -x^2 +1$ otherwise
 $x$ $f(x)$ 2 1 0 -1 -2
d.$f(x) = \sqrt x$ when $x \ge 0$ and $f(x) = -x +1$ otherwise
 $x$ $f(x)$ 2 1 0 -1 -2

2. For each function complete the function table and then create the corresponding mapping diagram and graph.

a. $f(x) = \frac 1 x$ when $x \ge 1$ and $f(x) = -x$ otherwise
 $x$ $f(x)$ 2 1 0 -1 -2

b.$f(x) = x+1$ when $x \ge -1$ and $f(x) = -x -1$ otherwise
 $x$ $f(x)$ 2 1 0 -1 -2

c.$f(x) = x^2 -2$ when $x \ge 1$ and $f(x) = -x$ otherwise
 $x$ $f(x)$ 2 1 0 -1 -2
d.$f(x) = x^2 -2$ when $x \ge -1$ and $f(x) = -x$ otherwise
 $x$ $f(x)$ 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. For each function complete the function table and then create the corresponding mapping diagram and graph.Verify that each is an implicit function for the equation $|y| -x^2 =0$.

a. $f(x) = x^2$ when $x \ge 0$ and $f(x) = -x^2$ otherwise
 $x$ $f(x)$ 2 1 0 -1 -2

b.$f(x) = x^2$ when $x \le 0$ and $f(x) = -x^2$ otherwise
 $x$ $f(x)$ 2 1 0 -1 -2

c.$f(x) = x^2$ when $x \ge 1$ and $f(x) = -x^2$ otherwise
 $x$ $f(x)$ 2 1 0 -1 -2
d.$f(x) = x^2$ when $x \le -1$ and $f(x) = -x^2$ otherwise
 $x$ $f(x)$ 2 1 0 -1 -2

6. For each function complete the function table and then create the corresponding mapping diagram and graph.Verify that each is an implicit function for the equation $|y| -|x|^3 =0$.

a.$f(x) = x^3$ when $x \ge 0$ and $f(x) = -x^3$ otherwise
 $x$ $f(x)$ 2 1 0 -1 -2

b.$f(x) = x^3$ when $x \ge -1$ and $f(x) = -x^3$ otherwise
 $x$ $f(x)$ 2 1 0 -1 -2

c.$f(x) = x^3$ when $x \le 0$ and $f(x) = -x^3$ otherwise
 $x$ $f(x)$ 2 1 0 -1 -2
d.$f(x) = x^3$ when $x \le -1$ and $f(x) = -x^3$ otherwise
 $x$ $f(x)$ 2 1 0 -1 -2

7. Suppose $f: N \rightarrow N$ is defined by $f(n) = 2^n$. Complete the function table and then create the corresponding mapping diagram and graph for $f$. Define the function $g$ for the domain $D = \{ m: m = 2^n$ for some $n \in N\}$ by $g(m) = n$, that is, $g$ is defined as the inverse function of $f$. Complete the function table and then create the corresponding mapping diagram and graph for $g$. Use the tables and mapping diagrams to check that $g$ is an inverse function for $f$ for the values in the tables .

 $n$ $f(n)$ 0 1 2 3 4

 $m$ $g(m)$ 1 2 4 8 16

8. Suppose $f$ is a continuous function with $f(x) = -x +a$ when $x \ge 1$ and $f(x) = x +1$ otherwise.
a. Determine the value of $a$. [ Use the fact that $f$ is continuous at $x=1$. ]
b. Use the value of  $a$  to find $f(-1)$ and $f(2)$.
c. Draw a graph and mapping diagram for $f$.
d. If possible, solve the equation $f(x) = 0$ and display the solutions on your mapping diagram.

9. Suppose $f$ is a continuous function with $f(x) = -x +3$ when $x \ge b$ and $f(x) = x +1$ otherwise.
a. Determine the value of $b$. [ Use the fact that $f$ is continuous at $x=b$. ]
b. Find $f(-1)$ and $f(2)$.
c. Draw a graph and mapping diagram for $f$.
d. If possible, solve the equation $f(x) = 0$ and display the solutions on your mapping diagram.

10. For each function $f: N \rightarrow N$ complete the function table and then create the corresponding mapping diagram and graph.

a. $f(0)=5$ and $f(n+1)=2(n+1) + f(n)$.
 $n$ $f(n)$ 0 1 2 3 4

b. $f(0)= -3$ and $f(n+1)= n - f(n)$.
 $n$ $f(n)$ 0 1 2 3 4

c. $f(0)=5$, $f(1)= 3$ and $f(n+2)=f(n+1) - f(n)$.
 $n$ $f(n)$ 0 1 2 3 4 5
d. $f(0)=0$, $f(1)= 1$ and $f(n+2)=2f(n+1) - f(n)$.
 $n$ $f(n)$ 0 1 2 3 4 5