Name:
/ 53 marks 
Score:
Date:
%  ISM:
 IB:
Block:
MATH HONORS 2: UNIT 2 ASSIGNMENT – Functions
A parent function is the simplest (i.e. not transformed) member in a family of functions. A child function in
the same family of functions is one or more transformations on the parent function. In this assessment, you
will graph eight different parent functions, as well as two child (transformed) functions for each parent
function. You will also graph and label the inverses of each parent function, and comment on any inverse
relationships between families of functions.
Note that all of your graphs must be drawn by hand as neatly as possible on millimeter graph paper, using a
ruler for the axes and any straight lines. Each set of axes should occupy one quarter of a page.
You may use your calculator to assist you in the graphing (using the table or graph function), but all your
graphs must be hand drawn.
Submit this original question sheet with your assignment at 7:30am on Thursday September 27th.
SECTION A: Parent Functions
(16M)
Graph the parent functions for each of the following eight families of functions on millimeter graphing paper.
Label the axes and the parent function for each graph, provide clear scales on the axes, and label the
coordinates of any important points (e.g. intercepts, endpoints, vertices, etc) and the equations of any
asymptotes.
You should also state the Domain AND Range for each function
1
x
a. Constant: f  x   2
e. Rational: r  x  
b. Linear: l  x   x
f.
c. Quadratic: q  x   x2
g. Square Root: s  x  
d. Cubic: c  x   x3
h. Exponential Growth: g  x   2x
Absolute Value: a  x   x
x
SECTION B: Child Functions
(16M)
Beside each parent function, draw another set of axes and graph two child functions, each one involving
exactly one different transformation of its respective parent function. For each graph, label the axes and
provide clear scales, label the graphs of the child functions with equations, and label the coordinates of any
important points (e.g. intercepts, endpoints, vertices, etc) and the equations of any asymptotes. Of the sixteen
child functions being graphed, there should be exactly two child functions involving each of the following
transformations:
a. Horizontal Translation (shift)
e. Vertical Translation (shift)
b. Horizontal Reflection (across the y-axis)
f.
c. Horizontal Expansion (stretch)
g. Vertical Expansion (stretch)
d. Horizontal Contraction (shrink)
h. Vertical Contraction (shrink)
Vertical Reflection (across the x-axis)
.
SECTION C: Inverse Functions
(17M)
In a different color, draw the inverse relation of each parent function onto the original parent graphs, and label
the coordinates of any important points (e.g. intercepts, endpoints, vertices, etc). Determine which families of
functions have inverses that are themselves functions and provide justification. Label the graphs of these
inverse functions with equations (some research may be required) and the equations of any asymptotes.
Discuss any inverse relationships among families of functions that you observed through completing this
assignment.
COMMUNICATION RUBRIC
(4M)
Level of Proficiency
Level
Key Question: Was I able
to understand the student’s
thinking or did I have to
make inferences about what
they were trying to do?
Exemplary
Proficient
Developing
Emerging
The lines of reasoning
are concise, logical and
complete.
The lines of reasoning
are usually concise,
logical and complete.
The lines of reasoning
were hard to follow or
redundant in some
places.
The student gave little or
no focused reasoning,
leaving too much
inference to the reader.
The student uses clear
and appropriate forms
of mathematical
representation.
The student uses
adequate forms of
mathematical
representation.
The student attempts to
use some appropriate
forms of mathematical
representation.
The student did not use
appropriate forms of
mathematical
representation.
The student consistently
uses appropriate notation
and terminology
throughout their work.
The student uses mostly
appropriate notation and
terminology with a
couple of minor
exceptions.
The student uses some
appropriate notation and
terminology, but there
are several errors.
The student uses little or
no appropriate notation
and terminology.
STUDENT SELF-EVALUATION
After the time allocated for writing this assessment has passed (or if you have finished early), answer the
following questions:
a. This assessment was (circle one):
TOO EASY
EASY
FAIR
HARD
b. Estimate the letter grade that you achieved on this assessment (e.g. A-, C+, etc.):
c. Which concepts did you have the most difficulty with during this assessment and/or this unit?
TOO HARD