Unit 2 Summative Test
Characteristics of Functions and Rate of Change
(PM)
Name: ___________________________________Student Number:_______________
OLG 1
Level
OLG 2
Level
OLG 4
Level
OLG 5
Level
OLG 1: Identifying Characteristics and Connecting Representations
Feedback
I can identify characteristics of functions from a graph and use them to sketch
the graph and/or create equation
I can identify transformations of all representations and connect transformations
to create equivalent forms (e.g. graph to equation, or equation to graph)
I can sketch the graph and state the equation of piecewise functions
OLG 2: Problems in Context
Feedback
I can connect relevant parts of contexts to algebraic models.
I can consider the context and the model to make predictions and judge the
reasonableness of my answers.
OLG 4: Evaluate and Simplify Expressions; Solve Equations
Feedback
I can determine even/odd symmetry algebraically
I can represent rates of change graphically & algebraically and calculate average
rate of change.
I can estimate instantaneous rates of change given the equation of a function
and a point and represent it graphically.
OLG 5: Communicate Mathematically
Feedback
I can use appropriate mathematical conventions & organisation
I can use appropriate mathematical terminology & vocabulary.
Sketches are clear, accurate, and labelled; Equation uses notation/convention
Formulas:
𝑓(𝑥) = 𝑓(− 𝑥)
− 𝑓(𝑥) = 𝑓(− 𝑥)
3
𝑦 = 𝑎[𝑘(𝑥 − 𝑑)] + 𝑐
4
𝑦 = 𝑎[𝑘(𝑥 − 𝑑)] + 𝑐
𝐴𝑅𝑂𝐶 =
𝑓(𝑥2)−𝑓(𝑥1)
𝑥2−𝑥1
1. a) Fill in the table of characteristics for the function, f(x), shown below. Estimate x and y values when
necessary.
Domain (set
notation)
Range (set
notation)
End
behaviours
Number of
turning point(s)
Number of
inflection
point(s)
Continuous or
Discontinuous
Interval of
increase
Interval of
decrease
Interval for
concave up
Interval for
concave down
b) Will the average rate of change of f(x) on the interval 𝑥ϵ[− 6, − 2] be positive, negative, or 0? Draw the
secant on the f(x) to support your answer.
2. State if the following functions are even, odd, or neither. Support your answer with a brief explanation for
(a) and algebra for (b).
a)
𝑓(𝑥)
b)
𝑔(𝑥) =
2𝑥
2
𝑥 −1
3. a) Sketch the piecewise function, h(x),
on the grid provided. It is not
necessary to show all the
transformations of the functions for
the sketch.
b) State the equation of the piecewise
function, p(x). (note: first function is
cubic)
4. Consider the quartic function, 𝑓(𝑥) =−
1
2
a) State the transformations of f(x).
b) Sketch f(x), using transformations, on the
grid provided.
Include 5 points.
4
(𝑥 + 2) + 6
5. The population of a certain fish in a region of the Atlantic
Ocean can be modelled by the function
3
2
𝑃(𝑥) =− 0. 2𝑥 − 1. 6𝑥 − 𝑥 + 14, where P is measured
in millions of fish and x is the number of decades.
(note: 1 decade is equivalent to 10 years).
a) Calculate 𝑃(2) and explain its meaning in context.
b) Calculate
𝑃(2)−𝑃(0)
and explain its meaning in context.
2−0
c) Determine the instantaneous rate of change at 1 decade. Conclude in context.
d) Explain the reasonableness of your rate of change answer in part (c).