Piecewise Activity
You may work in groups of up to 3 people. There will be one finished product turned in per group with all the names
below listed: Assign student A, B and C. Write your name next to the appropriate place.
A______________________
B______________________
C______________________
Pre-Study: http://www.mathsisfun.com/sets/functions-piecewise.html and http://coolmath.com/precalculusreview-calculus-intro/precalculus-algebra/07-graphing-piecewise-defined-functions-01.htm and
http://www.uiowa.edu/~examserv/mathmatters/tutorial_quiz/geometry/piecewisefunctions.html
1.
On your own individual graph, graph the following. If you need help, help each other!!!
Student A, graph f(x) = x + 5
Student B, graph f(x) = -2x – 1
Student C, graph f(x) = 2x – 9
2.
Now, fold your graph so you can only see the following domain for your function (domain is the x-values).
HELP EACH OTHER!!!
Student A, graph f(x) = x + 5 if x
-2.
Student B, graph f(x) = -2x – 1 if -2 < x
2.
Student C, graph f(x) = 2x – 9 if x > 2.
3.
Fit your three pieces together to form one graph. Tape/glue below.
y
11
10
9
8
4.
Now “redraw” each of your pieces on this same
graph.
7
6
5
4
Compare what you taped/glued down, to what you just drew.
3
2
Do you see any similarities or differences?
1
–11 –10 –9
–8
–7
–6
–5
–4
–3
–2
–1
–1
–2
–3
–4
What is the difference between < and
represent this on your graph?
How can you
–5
–6
–7
–8
–9
–10
–11
1
2
3
4
5
6
7
8
9
10
11
x
This is called a piecewise function. How many “pieces” are there to this function?
5. Try again, work together (aka-take turns and help
each other) to graph the following. Use the
same A, B, C student responsibilities.
y
11
10
9
8
Student A, f(x) = |x| if x < 2
Student B, f(x) = 2x-2 if 2 < x < 4
Student C, f(x) = 6 if x > 4
7
6
5
4
3
Did you remember your opened and closed circles?
2
1
Is this graph continuous?
If not, where in the domain and what type of
discontinuity is it?
–11 –10 –9
–8
–7
–6
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6
7
8
9
10
x
11
–2
–3
–4
–5
What is the domain of this graph?
“
“ “ range?
–6
–7
–8
–9
On what intervals is the graph increasing?
Decreasing?
–10
–11
y
6
5
6.
Graph f(x) = {
4
3
2
7. Find the following values
a. f(-4) =
b. f(-2) =
1
c. f(0)=
d. f(2) =
–6
–5
–4
–3
–2
–1
–1
–2
8. What are the x-intercepts of the function?
9. What is the relative maximum?
10. On which intervals is the function…
a. Increasing?
y-intercepts?
–3
–4
–5
Minimum?
b. decreasing?
–6
c. constant?
11. Holes?
12. What is the rate of change on the interval -5
x < -2
Discuss with your group…
13. What is something that you learned today and feel comfortable with?
14. What is something that you still need more work on?
1
2
3
4
5
6
x