Unit 3 Test ­ Polynomial Functions
Part A: Knowledge and Understanding (13 marks)
1) State the degree, leading coef f icient and end behaviours using inf inity notation
f or the f unction below. (3 marks)
f (x) = 6x4 + x + 2
2) State the equation of the quartic f unction in the graph below in f actored f orm. (3 marks)
3) Determine the x
− intercept(s) of the f unction y = 3(x − 2) − 243
4
(2 marks)
4) Determine whether the f unctions given are even, odd, or neither. (3 marks)
a)
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b) y = 6
c)
x
­2
­1
0
1
2
y
­36
­3
0
3
36
5) W rite an equation and sketch an example of a cubic f unction with the zeros at
3, 1 (order 2). (2 marks)
−
Part B: Application (11 marks)
1) Determine algebraically if the polynomial f unction f (x) = x4 + 2x + 3 is an even
f unction. (2 marks)
2) F ind the quotient and remainder of (x5 + 9x4
long division (2 marks)
−
− 2x
3) F ind the quotient and remainder of ( 3x4 + 5x3
synthetic division. (2 marks)
3
− 7x
2
+ 9x
− 5) ÷ (x
2
+ 4x + 2) using
− 1) ÷ (x + 4) using
− 27 and label all intercepts (3 marks)
− 15x + 6 has a zero when x =− 3. Determine the value
4) Graph the f unction f (x) = 2x3 + 9x2
5) T he f unction y = 4x3 + k x2
of k. (2 marks)
+ 7x2 + x
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Part C: Communication (11 marks)
1) W hat is the degree of the f unction represented with the table below? (2 marks)
x
y
­3
78
­2
22
­1
2
0
0
1
­2
2
­22
3
­78
2) W hen is it not possible to use synthetic division to divide polynomials? (1 mark)
3) Explain the dif f erence between an odd degree f unction and an odd f unction.
P rovide examples of each. (3 marks)
4) Describe the transf ormations that must be applied to create the f unction. (2 marks)
y=
− (3x − 12) − 2
3
5) W hich one of the f ollowing statements is f alse regarding synthetic division.
(1 mark)
a) one must be used as the coef f icient of any missing powers of the
v ariable in both the divisor and the dividend.
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b) a polynomial can only be divided by a polynomial of the same
degree or less.
c) synthetic division can only be used when the divisor is linear.
d) if the remainder of the synthetic division is zero, both the divisor
and the quotient are f actors of the dividend.
6) W hen dividing a 5th degree polynomial by a 3rd degree polynomial, what degree is
the quotient? W hat degree is the remainder? (2 marks)
Part D: Thinking (9 marks)
1) Sketch and state the equation of a f ourth degree polynomial f unction, with end
behaviours, as x
, y
, and three zero at f (3) = 0, f ( 2) = 0 and f ( 5) = 0.
(4 marks)
→− ∞ → ∞
−
−
2) T he graph below is a result of transf ormations applied to y = x3 . Determine the
equation of this transf ormed equation. (3 marks)
3) W rite an example of an odd polynomial f unction with 3 zeros in f actored f orm.
(2 marks)
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