Polynomial Functions - Introduction Worksheet Page 2
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31.5A – Polynomial Functions Introduction Practice Questions
1. Sketch the following functions. Check using graphing calculator if available.
rd
a) Positive 3
degree function that has zeros at -2, 0 and +2.
2
b) f(x) = x(x – 2)(x + 4)
nd
c) Negative 2
degree function that has zeros at -2 and +5
4
4
4
d) f(x) = x
e) f(x) = x
+ 3
f) f(x) = (x + 3)
4
3
2
2
2
g) f(x) = x
+ 3x
h) f(x) = x
(x +2) (x – 1)
i) f(x) = -(x + 3)
(x - 1)
3
2
2
i) g(x) = -x
j) g(x) = (x + 2)(x – 1)
k) g(x) = (x + 2)
(x – 1)
2
3
4
2
l) y = x
– x – 12
m) h(x) = -x
– 9x
n) m(x) = x
– 3x
+ 2
2. Determine the family of the functions, in form f(x) = k(x - a)(x - b)(x - c)(x + d), given the
information below;
rd
a) 3
degree function has zeros at -2, +2 and +3
th
b) 4
degree function touches the x-axis at -4 crosses x-axis at 0 and +2.
th
c) 5
degree function that touches x-axis at -2, -3 and crosses at +5
nd
d) 2
degree function that touches x-axis at +3
rd
e) 3
degree function with zeros at –½ , +¼ and -3
f) Use graph below
g) use graph below
3. Sketch the function f(x) = -x(x - 4)(x + 4) and then determine the values of any relative
maximums or minimums.
2
4. Sketch the function g(x) = x
(x – 2)(x + 2) and then determine the values of any relative
maximums or minimums.
Answers 1. a)
b)
c)
d)
e) check other graphs using graphing calculator
2
2
2
2
2. a) f(x)=k(x-2)(x+2)(x-3) b) f(x)=kx(x+4)
(x-2) c) f(x)=k(x+2)
(x+3)
(x-5) d) f(x)=k(x-3)
2
2
e) f(x)=k(2x+1)(4x-1)(x+3) f) f(x)=k(x+3)(x-2)
g) f(x)=k(x+4)(x+1)
(x-5)
3. f(2)=24 is a local max, f(-2)=-24 is a local min 4. g(0)=0 is local max, g(-1)=-3 and g(1)=-3 are local mins,
but if you use the calculator to trace you can more accurately see g(-1.4)=-3.9 and g(1.4)=3.9
1.5A – polynomial functions Introduction
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