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Characteristics of Functions Unit Assignment
DROPBOX:Characteristics of Functions Unit Assignment
This is your first assignment in the course, as you progress through the course you will need
to complete calculations as part of your practice and assignments. Below is a list of
calculators that are pre-approved for use during the exam. Before you begin the course, it is
a good idea to make sure that the calculator you are using is approved for use in the exam.
You may use any scientific, non-programmable, non-graphing calculator. Select your
calculator’s brand and model from the drop-down menu to confirm if your calculator is
approved or not.
Select a Brand Select a Model
Calculator Brand Calculator Model
Find your calculator in the drop-down list.
Your calculator is not in the list?
Email your department head with your calculator’s brand, model name, and image to
confirm it is acceptable.
Mathematics Department: Ron.Will@vhs.ucourses.com
Communication (10 Marks)
The following questions are to be answered with full solutions. Be sure to focus on proper
mathematical form, including:
One equal sign per line
Equal signs in each question lined up vertically with each other
No self-developed short form notation
One step or idea per line (do not do steps in your head that are not written down; each
line must represent a step-by-step progression from question to answer)
Knowledge & Understanding (60 Marks)
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1. Simplify. (2 each)
2. Find the inverse of the following function, show all work: (6)
3. The graph is shown below: (10)
a. Is the above relation a function? Justify your answer.
b. Graph the inverse of the relation. Just submit the coordinates of the graph.
c. Is the inverse a function? Justify your answer.
4. Consider the equation . (10)
a. What is the base (original) function?
b. Describe the series of transformations from the base function to
c. Write the equation in the function notation, .
5. Sketch an example of a relation with Domain and Range
. Is your sketch a function? Explain your answer. (5)
6. Determine the quadratic function of the following: A parabola with vertex (0,-4) and
passing through the point (1,-3). (5)
2 27 + 5 − 3 + 4
−− √ √8 18
−− √ 12
−− √
(2√8 + 5 12)
−− √
f (x) = -2 3x − 1 − 5, x ≥
−−−−− √
y = -2 3x − 12 − 5
−−−−−− √
y = -2 3x − 12 − 5
−−−−−− √
y = af (k (x − d)) + c
{x|x ∈ R}
{y|y ≥ -5, y ∈ R}
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7. Determine, through investigation, the equations of the lines that have a slope of 2 and
that intersect the quadratic function once; twice; never. (15)
8. Simplify: State the restrictions if any. (5)
Thinking and Application (30 Marks)
1. For security, a credit card number is coded in the following way, so that it can be sent
as a message. Subtract each digit from 9. (8)
a. Code the credit card number 3201 2342 3458 0931.
b. A coded credit card number is 2341 0135 7923 0133. What is the original credit card
c. Find if represents a single input digit. What is the domain of ?
d. Find . What is the domain of ?
2. The sum of two numbers is 28. Find the numbers if the sum of their squares is a
minimum. (6)
3. Bob and Jack enter a 1000 km bicycle race. Bob cycles 4 km/h faster than Jack, but his
bicycle gets a flat tire, which takes 30 minutes to repair. If both of them finish the race in
a tie, then how fast was each boy cycling? (6)
4. The following function gives the height h meters, of a batted baseball as a function of
the time, t seconds, since the ball was hit. (10)
a. What is the physical significance of the 5.875? Prove this is true.
b. Determine the following characteristics: axis of symmetry, direction of opening,
and intercepts, vertex, minimum/maximum, (hint: Write in standard form).
c. Plot the graph. (you do not need to submit this)
d. What is the physical significance of the h-intercept of the graph?
f (x) = x (x − 6)
x +6x+5
x +7x+12
x +2x−8
x −25
x −x−2
x −2x−15
f (x) x f (x)
f (x)
-1 f (x)
h = -4.5t + 13.5t + 5.875
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e. What is the geometric significance of the left t-intercept of the graph? Why does this
point have no real physical meaning?
Assessment OF: This assignment will be evaluated for a grade or mark that will contribute to your overall final mark in this course.