Mathematical Analysis
Mini-Project #1: Piecewise Functions
Name:
Due Date:
In this project, you will create a piecewise function that has the characteristics listed below. You will write
the piecewise function algebraically (don’t forget to include the domain!), and you will graph the piecewise
function on graph paper. Show all work and explain why your function satisfies the required conditions.
(This part does not need to be a report/paper, simply a description or summary.)
Step 1: Pick four numbers (any real numbers, positive or negative, but all most be different and at least one
must be negative). Be mindful when choosing numbers!
A=
B=
C=
D=
Step 2: Create a piecewise function that follows the following conditions (use your numbers from Step 1):
a)
b)
c)
d)
A hole at x = A
A vertical asymptote at x = B
A jump at x = C
A horizontal asymptote at y = D
Step 3: Graph your piecewise function neatly on graph paper (or on a computer program if you so choose).
Step 4: Be sure all of your work is shown neatly and easy to follow. Write a brief description/summary
explaining why your function satisfies the required conditions. Include explanations of how to find the
vertical and horizontal asymptotes of a function and how to create a hole or a jump.
Things to think about when creating your function and writing your summary:
 How can you create a hole in the graph? What must happen in your function in order for a hole to be
present? (Hint: If you graph the function on your graphing calculator, the hole will not appear, so you
need to know what makes a function have a hole and draw it in by hand.)
 What kinds of functions give you a vertical asymptote? How is a vertical asymptote defined or
restricted?
 How can you create a jump in the graph? Think about our notes on transformations of graphs.
 What do you need in order to create a horizontal asymptote? Think about our notes on rational
functions.
Project Rubric
Topic
Graph and Function: Hole at x = A
Graph and Function: Vertical asymptote at x = B
Graph and Function: Jump at x = C
Graph and Function: Horizontal asymptote at y = D
Correct domains in the function that match the graph
Brief explanation
Professionalism – neat, all work shown, turned in on time
TOTAL
Points
Possible
6
6
6
6
8
10
3
45
Points
Earned
*SAVE THIS SHEET! YOU WILL TURN IT IN WITH YOUR PROJECT FOR THE RUBRIC!*