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WorksheetsCubic Functions Graphing and Evaluating
Total questions: 25
Worksheet time: 2hrs 5mins
Name
Class
Date
1.
What is the y-intercept of the following cubic function?
a)
(1, 0)
b)
(0, 2)
c)
(-1, 0)
d)
(2, 0)
2.
Determine the roots of the polynomial.
f(x) = (x+1)(x-4)(x+2)
f(x) = (x+1)(x-4)(x+2)
a)
1, 4, 2
b)
-1, -4, -2
c)
1, -4, 2
d)
-1, 4, -2
3.
Describe the transformation of the graph y = -(x - 4)3 + 5
a)
Up 5 and Left 4
b)
Reflect x-axis, Left 4, Up 5
c)
Reflect x-axis, Right 4, Up 5
d)
Right 4 and up 5
4.
Describe the transformation of the graph y = (x)3 + 6
a)
Right 6
b)
Left 6
c)
Up 6
d)
Down 6
5.
Describe the transformation of the graph y = - ½(x + 4)3 - 1
a)
Left 4 and Down 1
b)
Reflected x-axis, Down 1, Left 4, Compression by a factor of 1/2
c)
Reflected x-axis, Down 1, Left 4, Stretch by 1/2
d)
Reflected x-axis, Up 1, Right 4, Compression by a factor of 1/2
6.
Determine the roots of the polynomial.
f(x) = (x-2)(x+3)2
f(x) = (x-2)(x+3)2
a)
2, 3
b)
2, -3
c)
-2, 3
d)
-2, 3, 3
7.
Determine the roots of the polynomial.
f(x) = -x(x+1)(x-3)
f(x) = -x(x+1)(x-3)
a)
-1, 3
b)
0, -1, 3
c)
1, -3
d)
0, -3, 1
8.
What is the Domain of ALL Cube Root Functions in interval notation?
a)
(−∞,∞)
b)
−∞<x<∞
c)
(−∞,0]
d)
All Cube Root Functions are different.
9.
What is the Range of ALL Cube Root Functions in interval notation?
a)
(−∞,∞)
b)
−∞<y<∞
c)
(−∞,0]
d)
All Cube Root Functions are different.
10.
Which point does not represent a zero of a polynomial?
a)
(-2, 0)
b)
(-1, 0)
c)
(0, 4)
d)
(2, 0)
11.
Which is the factored form of the polynomial function?
a)
(x-2)(x-1)(x+1)(x-2)
b)
(x-2)(x-1)(x+1)(x+2)
c)
(x-2)(x-1)(x+1)(x+2)(x-4)
d)
(x-2)(x-1)(x+1)(x+2)(x+4)
12.
What could be the equation for this graph?
a)
y = -2x3 + 1x + 3
b)
y = (x - 2)(x + 1)(x + 3)
c)
y = (x + 2)(x - 1)(x - 3)
d)
y = -2x2 + 1x + 3
13.
What are the x-intercepts of the following function?
y = (x - 1)(x +3)(x - 4)
y = (x - 1)(x +3)(x - 4)
a)
1, 3 and 4
b)
2, 1, -3, and 4
c)
-1, 3, and -4
d)
1, -3, and 4
14.
What is another way to say "where a function crosses the x-axis"?
a)
x-intercept
b)
zero
c)
root
d)
all of these.
15.
What are the
zeros of the polynomial
y = (x + 4)(x + 1)(x - 3)?
zeros of the polynomial
y = (x + 4)(x + 1)(x - 3)?
a)
-4, -1, 3
b)
3, -3, 4, 1
c)
4, 1, -3
d)
3, -4, -1, 3
16.
What could be the equation for this graph?
a)
y = -2x3 + 1x + 3
b)
y = (x - 2)(x + 1)(x + 3)
c)
y = (x + 2)(x - 1)(x - 3)
d)
y = -2x2 + 1x + 3
17.
What is the range of ALL cubic functions expressed as an inequality?
a)
[-∞, ∞]
b)
(-∞,∞)
c)
-∞≤y≤∞
d)
-∞<y< ∞
18.
What is the domain ALL cubic functions expressed as an inequality?
a)
(-∞,∞)
b)
-∞<x< ∞
c)
(-∞, 0]
d)
-∞<y< ∞
19.
What is the point of inflection for the following cubic function?
a)
(-3, -1)
b)
(0, -4)
c)
(-1, -3)
d)
(0, 0)
20.
What is the factored form for the following cubic function?
a)
x(x - 3)(x - 4)
b)
x(x + 3)(x + 4)
c)
x(x - 3)(x + 4)
d)
(x + 3)(x - 3)(x - 4)
21.
What is/are the zero(s) of the function?
a)
x = 4, x = 1, x = -2
b)
x = -4, x = -1, x = 2
c)
y = -2
d)
(0, -4), (0, -1), (0, 2)
22.
Identify the x-intercepts:
a)
No x-intercpts
b)
x = -2, x = 3, x = -8
c)
x = -2, x = 3
d)
x = -2, x = 3, x = 8
23.
What are all the y-intercepts?
a)
(0, -6.25)
b)
(-3,0), (-2,0), (2,0), (3,0)
c)
(0, 36)
d)
(-∞, ∞)
24.
Using you CALCULATOR, What are the zeros of the function f(x) = -2x3 - 4x2 + 6x?
a)
x = 0, -2, -3, 1
b)
x = -3, 1
c)
x = 0, 3, -1
d)
x = 0, -3, 1
25.
Which set of factors has x-intercepts at 5, -1, 2?
a)
(5x)(-1x)(2x)
b)
(x-5)(x+1)(x-2)
c)
(x-5)(x-1)(x-2)
d)
(x+5)(x-1)(x+2)
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