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.
Download these exercises as a .pdf file: Worksheet.OW.pdf.
  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 c  and 1 d,  find any values of $a$ where $f(a) = 0$.

  4. For the functions in problem 2 c  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