TEST SUMMARY
TEST 1: Name
Knowledge &
Understanding
Inquiry
Communication
Application
20
20
20
12
SHOW ALL YOUR WORK: FULL MARKS WILL ONLY BE GIVEN IF ALL STEPS ARE SHOWN.
Part A: Knowledge & Understanding (20 marks)
Multiple Choice: Each of the following questions is followed by four (4) suggested answers.
Circle the correct answer. (10 marks)
1. Which of the following statements about a polynomial function is false?
a. A polynomial function of degree n has at most n turning points.
b. A polynomial function of degree n may have up to n distinct zeros.
c. A polynomial function of odd degree may have at least one zero.
d. A polynomial function of even degree may have no zeros.
2. If the leading coefficient of an odd-degree polynomial function is positive, then the function extends
from the third quadrant to the first quadrant; that is, as
a. x→,y→− and as x→−,y→
b. x→−,y→ and as x→,y→−
c. x→−,y→− and as x→,y→
d. x→−,y→− and as x→,y→−
3. What is the degree and lead coefficient of f(x) = −x + 5x − 6x + 10?
2
a) degree 1 with a lead coefficient of –1
b) degree 3 with a lead coefficient of –6
c) degree 3 with a lead coefficient of –1
d) degree 6 with a lead coefficient of –1
3
4. Which polynomial function would have the end behaviour of as x → , y → ?
a) f(x)=7x5 −8x4 −2x3 +x2 +3x−2
b) f(x)=−6x3 +3x2 +x−11
c) f(x)=−4x2 +3x4 −6x3 +2x+8
d) f(x)=x3 −9
5. Use end behaviours, turning points, and zeros to determine which graph represents the polynomial
equation y=3x3 +5x2 −x+3.
a)
b)
c)
d)
6. What is the maximum number of turning points that the polynomial function f(x) = 4x7 + 9x5 − 3x4 + 2x2
− 5 can have?
a. 0
b. 3
c. 2
d. 6
7. If any of the linear factors of a polynomial function are squared, then which of the following is not true
of the corresponding x-intercepts?
a) The x-intercepts are turning points of the curve.
b) The x-axis is tangent to the curve at these points.
c) The graph passes through the x-axis at these points.
d) The graph has a parabolic shape near these x-intercepts.
8. Which of the following is NOT a factor of 𝑥3 +2𝑥2 −5𝑥−6?
a) x–2
b) x–3
c) x+3
d) x+1
9. When P(x)=2𝑥3 −3𝑥2 +8𝑥−12 is divided by x–1 the remainder is
a) 5
b) 0
c) -3
d) -5
𝑥−1
10. Which is true for the rational function 𝑓(𝑥) = 2𝑥+5
a) The y-intercept is -1
b) The x-intercept is -1
c) The vertical asymptote is x = 2.5
d) The horizontal asymptote is y = 0.5
SHORT ANSWER – Fill in the table
(10 marks)
Polynomial
𝑦 = 2𝑥3 + 3𝑥 − 1
𝑦 = 5𝑥 − 6
𝑦 = 𝑥3 − 2𝑥2 − 5𝑥4 + 3
𝑦 = −3𝑥5 + 2𝑥3 − 𝑥 − 1
𝑦 = 21 − 2𝑥 + 4𝑥2 − 6𝑥3
Degree
Leading Coefficient
Part B: Inquiry (20 marks)
𝑥 2 +𝑥−12
1. Given 𝑓(𝑥) = (𝑥−1)(𝑥+4) determine the equations of all asymptotes, coordinates of hole(s), yintercept and zeros. (6 marks)
2. i) State the equations of the horizontal asymptotes of the following functions.
ii) Determine the end behaviours of the graphs near the horizontal asymptotes.
Show your work. (4 marks)
a) 𝑓(𝑥) =
2𝑥+3
𝑥−1
b) 𝑓(𝑥) =
𝑥+3
2𝑥 2 +5𝑥+2
3. Complete the following table: (10 marks)
Graph of
Function
Even or Odd
Degree?
Sign of
Leading
Coefficient
Part C: Communication (20 marks)
1. Factor completely (6 marks)
𝒙𝟑 −𝟑𝒙𝟐 −𝟒𝒙+𝟏𝟐
Domain and
Range
Symmetry
End Behaviour
2. For each function, complete the chart and sketch a graph of the function labelling key
points. (7 marks each)
a) 𝑓(𝑥) = (𝑥 + 1)(𝑥 − 3)(𝑥 + 2)
Degree
Leading Coefficient
End Behaviour
𝒙-intercepts
𝒚-intercept
b) 𝑔(𝑥) = −𝑥(𝑥 + 1)(𝑥 + 2)2
Degree
Leading Coefficient
End Behaviour
𝒙-intercepts
𝒚-intercept
Part D: Application (12 marks)
1. When 2𝑥4 −𝑘𝑥2 +𝑘𝑥+2 is divided by x+2, the remainder is 10. Find the value of k. (6
marks)
2. Write an equation for the function that results from the given transformations. (3 marks
each)
3
a) The function 𝑓(𝑥) = 𝑥4 is compressed vertically by a factor of 5, stretched horizontally by a
factor of 2, reflected horizontally in the 𝑦-axis, and translated 1 unit up and 4 units to the left.
1
b) The function 𝑓(𝑥) = 𝑥3 is compressed horizontally by a factor of 4 , stretched vertically by a
factor of 5, reflected vertically in the 𝑥-axis, and translated 2 units to the left and 7 units up.