Chapter 1 Practice Test
(page 1)
For questions 1 and 2, select the best
answer.
1. Which statement is true for a polynomial
function? For those that are not true,
provide a counterexample.
A with degree 2 and a positive leading
coefficient, the graph extends from
quadrant 3 to quadrant 4
B with degree 5 and a negative leading
coefficient, the graph extends from
quadrant 2 to quadrant 4
C with degree 4 and a negative leading
coefficient, the graph extends from
quadrant 2 to quadrant 1
D with degree 3 and a positive leading
coefficient, the graph extends from
quadrant 2 to quadrant 1
2. Which statement is true? For those that
are not true, provide a counterexample.
For the function y = –2(4x – 8)3,
compared to the base function y = x3,
there is
A a reflection in the y-axis
B a horizontal stretch by a factor of 4
C a horizontal translation 8 units to the
right
D a vertical stretch by a factor of 2
3. Match each graph of a polynomial
function with the corresponding equation.
Justify your choice.
i) y = –x5 – 3x2 + 7
ii) y = x4 + 6x3 + 11x2 + 6x
iii) y = x3 + x2 – 4x + 1
a)
b) Window: x  [–4, 2], y  [–5, 10]
c) Window: x  [–4, 4], y  [–10, 10]
4. For each polynomial function in question
3 determine which finite differences are
constant and find the values of the
constant differences.
5. A quartic function has zeros – 4, –2, and
1(order 2).
a) Write a general equation for a
polynomial function that satisfies this
description.
b) Determine an equation for a function
with the zeros given above that passes
through the point (–3, 12).
c) Sketch the function found in part b).
Then, determine the interval(s) where
the function is positive and the
interval(s) where the function is
negative.
6. a) Identify the parameters a, k, d, and c in
the polynomial function
y = 4(3x – 12)2 – 2.
b) Describe how each parameter
transforms the base function y = x2.
c) State the domain, range, vertex and the
equation of the axis of symmetry of
the transformed function.
c) Sketch graphs of the base function and
the transformed function on the same
set of axes.
(page 2)
7. Transformations are applied to y = x4 to
obtain the graph shown. Determine its
equation.
Window: x  [–4, 2], y  [–6, 6]
8. a) The population, P, of a town t years
from now can be modelled by the
function P(t)= 6t3 – 100t + 25 000.
Describe the key features of the graph
representing the function, if no
restrictions are considered.
b) What is the current population of the
town?
c) What is the value of the constant finite
differences for the population
function?
d) What are the restrictions that should be
considered?
e) Use Technology When will the town
have a population of approximately
120 000 people? Round your answer
to one decimal place.
9. A stone is thrown from the top of a
bridge into a lake below such that its
height, h, in metres, can be modelled by
the function h(t) = 60 – 8t – 4.9t2, where t
is measured in seconds.
a) Determine the average rate of change
of the height of the stone in the first
2.5 s after it was dropped. Round your
answer to one decimal place.
b) Estimate the instantaneous rate of
change of the height of the stone after
2.5 s.
c) Interpret your answers from parts a)
and b).
Chapter 1 Practice Test ANSWERS
1. B
2. D
3. i) and c): odd degree, negative leading
coefficient; ii) and b): even degree,
positive leading coefficient; iii) and a):
odd degree, positive leading coefficient
4. i) fifth; –120 ii) fourth; 24 iii) third; 6
5. a) y = a(x + 4)(x + 2)(x – 1)2, a  0
3
b) y =  (x + 4)(x + 2)(x – 1)2
4
c)
positive −4 < x < −2;
negative x < −4, −2 < x < −1, x > 1
6. a) a = 4: a vertical stretch by a factor of 4;
k = 3: a horizontal compression by a
1
factor of ; d = 4: a horizontal
3
translation
4 units to the right; c = –2: a vertical
translation 2 units down
b) {x  } ; { y  , y  2} ; vertex: (4, –
2); axis of symmetry: x = 4
c)
7. y = –(x + 2)4 + 4
8. a) cubic function with a positive leading
coefficient ; end behaviour: quadrant 3
to 1; no point or line symmetry;
x-intercept –16.4; y-intercept 25 000;
no local maximum or minimum points
b) 25 000
c) 36
d) t  0, P(t)  0
e) 25.3 years
9. a) –20.3 m/s
b) –32.5 m/s
c) Both values are negative because the
stone is moving downward towards
the ground.