PreCalculus 11 Chapter 7/8 Project
Name______________________
Paint – by – Functions
*This project is NOT optional – it takes the place of your chapter test and will be worth approximately 50% of
the chapter’s mark.
Your mission: create a pretty picture composed of functions. Your picture must include:
 1 linear functions
 1 quadratic functions
 1 “linear” absolute value function
 1 “quadratic” absolute value function
 2 reciprocal functions (the original versions do not have to be shown)
the absolute value or reciprocal function of any general “f(x)” functions that are drawn but not described
by equations (to allow you to draw whatever shapes you need
 1 linear-quadratic or quadratic-quadratic system. Your description should include intersection points,
graphically highlighted and verified algebraically.
-
You’ll hand in:
a) Your lovely picture. Flattering portraits of your
math teacher may get extra credit.
b) A page of functions, with domain/range
statements matching the criteria above, that
created your picture.
Descriptions:
1a.
y
1
( x  25)2  45
1b. y 
1
( x  25) 2 45
D: 22< x < 27
D: 30 < x < 35
.
.
2a. y = 0.22(x-90) 2 + 100 D: 55<x<65
2b y = 0.22(x-94) 2 + 100 D: 65<x<75
.
.
3. y = 0.33(x-30) 2 + 80
y = 0.25(x-30) 2 + 70 D: 0<X<60
Intersection points:
0.33(x-30) 2 + 80 = 0.25(x-30) 2 + 70
0.33(x-30) 2 + 10 = 0.25(x-30) 2
0.33x2 + 20x + 300 = 0.25x2+15x+225
…. Intersects: (0,40) and 55,45)
Use domain/range statements to limit the extent of the functions on the page, to hide parts of the functions that
shouldn’t appear.
Use pencil crayons, highlighters, etc. to color the functions and regions of your picture.
The origin can be either in the lower-left corner or elsewhere on the page; the page can be oriented landscape or
portrait.
You can collaborate with a partner, but you must each produce your own project.
Hand in the picture, plus the marking guide. Fill in your own marking guide with your most honest assessment
of your work.
Technology option: using the Desmos online calculator or another digital tool re-create your picture digitally.
This option earns 5% in bonus marks. Example:
Your functions will be different from these,
obviously, to meet the criteria above. Note the
domain statements that precede each function.
PrintScreen and print your digital version and
hand in with your paper version.
Marking Guide:
1
Linear Function
Absolute
Value
Functions
Major Error (in graphing or
domain/range statement)
2
Minor Error (in graphing or
domain range statement)
3
No Errors:
Initial function represented
correctly
Function is transformed
Domain / Range stated
Quadratic Function
General function
y  f ( x)
Linear Function
Reciprocal
Functions
Major Error (in graphing or
domain/range statement)
Minor Error (in graphing or
domain range statement)
No Errors:
Initial function represented
correctly
Function is transformed
Domain / Range stated
Major Error in calculation
Minor Error in Calculation
Used relevant mathematical
concepts efficiently
Major Error in calculation
Minor Error in Calculation
Used relevant mathematical
concepts efficiently
Quadratic Function
General function
y  f ( x)
LinearQuadratic
Systems
QuadraticQuadratic
Systems
Technology
and
Visualization
Problem
Solving
Graph is not appropriate or
major errors.
Student required substantial
assistance or missed asking
assistance which would have
improved their project
Constructs appropriate
graphs; may contain minor
errors
Student sought minor, but
necessary assistance
Constructs appropriate graphs
effectively
Student independently created
functions that represent each
shape, checking correctness
as necessary