Module 11 Lesson 3
Polynomial Functions – Quiz
Some questions are doubled up if a pool wants to be set up to
randomize the questions.
Question 1: Short answer/Fill in the blank
Find the limit graphically:
lim 𝑥 2 − 2𝑥
𝑥→3
Answer: 3
Feedback: Make sure that you have graphed your function carefully. Use
an online graphing calculator, such as https://www.desmos.com/calculator if
you do not have a calculator.
Look at the y value for x = 3.
Question 2: Short answer/Fill in the blank
Find the limit graphically:
lim 𝑥 3 − 3𝑥 2
𝑥→−1
Answer: -4
Feedback: Make sure that you have graphed your function carefully. Use
an online graphing calculator, such as https://www.desmos.com/calculator if
you do not have a calculator.
Look at the y value for x = -1.
Question 3: Multiple Choice with multiple Answers
What kind of transformation does 𝑦 = 16𝑥 4 − 5 have? Please check all that
apply
A. Horizontal stretch of 16
B.
C.
D.
E.
F.
G.
H.
Horizontal stretch of 1/2
Vertical stretch of 16
Vertical stretch of 1/2
Horizontal shift of 5 right
Horizontal shift of 5 left
Vertical shift of 5 down
Vertical shift of 5 up
Answers: B, C, and G
Feedback: Try graphing the polynomial on your calculator to see which
answers apply.
Question 4: Multiple Choice with multiple Answers
What kind of transformation does 𝑦 = −2(𝑥 − 3)5 + 1 have? Please check all
that apply.
A.
B.
C.
D.
E.
F.
G.
H.
Reflects across the y-axis
Reflects across the x-axis
Horizontal stretch of 1/2
Vertical stretch of 2
Horizontal shift of 3 right
Horizontal shift of 3 left
Vertical shift of 1 down
Vertical shift of 1 up
Answers: B, D, E, and H
Feedback: Try graphing the polynomial on your calculator to see which
answers apply.
Question 5: Multiple Choice
Graph the function: 𝑓(𝑥) = 3𝑥 4 − 2𝑥 3 − 5𝑥 2 + 𝑥 − 1
Which is the function that is the vertical reflection of this function?
A.
B.
C.
D.
𝑓(𝑥) = −3𝑥 4 + 2𝑥 3 − 5𝑥 2 − 𝑥 − 1
𝑓(𝑥) = 3𝑥 4 + 2𝑥 3 − 5𝑥 2 − 𝑥 − 1
𝑓(𝑥) = −3𝑥 4 + 2𝑥 3 + 5𝑥 2 − 𝑥 − 1
𝑓(𝑥) = −3𝑥 4 − 2𝑥 3 − 5𝑥 2 − 𝑥 − 1
Answer: B
Feedback: To find this function, take your original function and plug in “-x”
where you see “x” and evaluate.
Question 6: Short answer
Describe the end behavior of this polynomial function:
𝑦 = −3𝑥 5 − 2𝑥 4 + 6𝑥 − 3
Answer: As 𝑥 → ∞, 𝑦 → −∞ and as 𝑥 → −∞, 𝑦 → ∞
Question 7: Multiple Choice
Which answer best describes the end behavior of this polynomial function:
𝑦 = 2𝑥 6 + 4𝑥 4 − 𝑥 3 + 6𝑥
A.
B.
C.
D.
As
As
As
As
𝑥
𝑥
𝑥
𝑥
→ ∞, 𝑦
→ ∞, 𝑦
→ ∞, 𝑦
→ ∞, 𝑦
Answer: C
→ ∞ and as 𝑥 → −∞, 𝑦 → −∞
→ −∞ and as 𝑥 → −∞, 𝑦 → ∞
→ ∞ and as 𝑥 → −∞, 𝑦 → ∞
→ −∞ and as 𝑥 → −∞, 𝑦 → −∞
Feedback: What is the degree of the polynomial? Is it even or odd?
Remember the 2 x 2 table you filled out in your notes? This would be a
great resource to help with this problem.
Question 8: Multiple Choice
Which answer best describes the end behavior of this polynomial function:
𝑦 = −3𝑥 2 − 2𝑥 + 1
A.
B.
C.
D.
As
As
As
As
𝑥
𝑥
𝑥
𝑥
→ ∞, 𝑦
→ ∞, 𝑦
→ ∞, 𝑦
→ ∞, 𝑦
→ ∞ and as 𝑥 → −∞, 𝑦 → −∞
→ −∞ and as 𝑥 → −∞, 𝑦 → ∞
→ ∞ and as 𝑥 → −∞, 𝑦 → ∞
→ −∞ and as 𝑥 → −∞, 𝑦 → −∞
Answer: D
Feedback: What is the degree of the polynomial? Is it even or odd?
Remember the 2 x 2 table you filled out in your notes? This would be a
great resource to help with this problem.
Question 9 Multiple Choice
What is the largest degree of this polynomial?
A. Third
B. Fourth
C. Fifth
D. Sixth
Answer: C
Incorrect Feedback: How many turns does the polynomial have?
Remember that a polynomial has one less turn that the degree.
Question 10: Multiple Choice
What is the degree of this polynomial:
𝑦 = 1 + 5𝑥 3 − 2𝑥 4 + 9𝑥
A.
B.
C.
D.
Fifth
Fourth
Third
Second
Answer: B
Incorrect Feedback: Remember that polynomials should be in
descending order by exponent. The degree is then the highest exponent
in the function.
Question 11: True or False
This function is a polynomial:
𝑦=
1
𝑥
Answer: False
Incorrect Feedback: By definition, a polynomial has exponents that are
non-negative integers.
Question 12: Short answer
State the domain and range of this polynomial in proper interval notation:
Answer: Domain: (-∞, ∞)
Range: (-∞, ∞)
Question 13: Short answer
State the domain and range of this graph in proper interval notation:
Answer: Domain: [0, ∞)
Range: (-∞, ∞)
Question 14: Multiple Choice with multiple Answers
Given the polynomial 𝑦 = −9𝑥 5 − 5𝑥 + 1, select all names from the list that
accurately describe this polynomial.
A.
B.
C.
D.
E.
F.
Quadratic
Quartic
Quintic
Monomial
Binomial
Trinomial
Answers: C & F
Feedback: There are more than one correct answer. Remember that
polynomials are named by degree and by number of terms.
Question 15: Multiple Choice with multiple Answers
Given the polynomial 𝑦 = 3𝑥 3 , select all names from the list that accurately
describe this polynomial.
A.
B.
C.
D.
E.
F.
Quadratic
Cubic
Linear
Monomial
Binomial
Trinomial
Answers: B and D
Feedback: There are more than one correct answer. Remember that
polynomials are named by degree and by number of terms.