Free Printable Test 4 REVIEW: Cubic/Cubed Root & Polynomial Functions

1.

Which function matches the graph pictured?

a)

f(x) = − ∛ (x + 3) − 1

b)

f(x) = − ∛(x - 3) − 1

c)

f(x) = ∛(x + 3) − 1

d)

f(x) = ∛(x - 1) + 3

2.

What is the center point or "vertex" of the function?

a)

(5,-3)

b)

(5,3)

c)

(-5,-3)

d)

(-5,3)

3.

Identify the Transformations.

a)

Down 2

b)

Up 2

c)

Reflection and stretch by 2

d)

Reflection and down 2

4.

Determine the end behavior of the polynomial function.

a)

Up left, up right

b)

Down left, down right

c)

Up left, down right

d)

Down left, up right

5.

Determine the end behavior of the function:

f(x) = 3x² + 5x - 9

a)

UP and UP

b)

DOWN and DOWN

c)

UP and DOWN

d)

DOWN and UP

6.

Determine the end behavior of the function:

f(x) = 4 + 3x - 6x⁷ + 3x⁴

a)

UP and UP

b)

DOWN and DOWN

c)

UP and DOWN

d)

DOWN and UP

7.

In the above graph complete the following end behavior: (f(x)=y)

As x --> -∞, f(x) --> ____

As x --> +∞, f(x) --> ____

a)

As x --> -∞, f(x) --> -∞ ; As x --> +∞, f(x) --> -∞

b)

As x --> -∞, f(x) --> +∞ ; As x --> +∞, f(x) --> -∞

c)

As x --> -∞, f(x) --> -∞ ; As x --> +∞, f(x) --> +∞

d)

As x --> -∞, f(x) --> +∞ ; As x --> +∞, f(x) --> +∞

8.

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient

a)

Leading Coefficient Positive
Degree - Even

b)

Leading Coefficient Positive
Degree - Odd

c)

Leading Coefficient Negative
Degree - Even

d)

Leading Coefficient Negative
Degree - Odd

9.

Classify the polynomial by its degree & number of terms:

f\left(x\right)=2x^4-4x+7

a)

Quartic Binomial

b)

Quadratic Trinomial

c)

Cubic 4-term polynomial

d)

Quartic Trinomial

10.

Find the product:
(5n-8)(5n+8)

a)

25n²-64

b)

10n²

c)

5n²+16

d)

16

11.

Find the product:
(2x+3)²

a)

2x+3+2x+3

b)

4x²+12x+9

c)

4x²+9

d)

16x²+9

12.

Classify the polynomial by degree & number of terms:

73

a)

Linear Monomial

b)

Constant Binomial

c)

Quadratic Monomial

d)

Constant Monomial

13.

What is the perimeter for the given rectangle:

a)

6x³ - 9x² + 10x - 15

b)

6x² + 1x - 15

c)

6x² + 4x + 4

d)

6x³ + 1x² - 15x

14.

Classify the polynomial by degree & number of terms:

-9x^3

a)

Linear Monomial

b)

Cubic Binomial

c)

Cubic Monomial

d)

Quadratic Trinomial

15.

Find the difference.
(3- 2x + 2x²) - (4x -5 +3x²)

a)

x_² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

16.

(2x + 3)(x² + 4x + 1)

a)

2x³ + 10x² + 14x + 4

b)

2x³ + 11x² + 14x + 3

c)

-2x³ - 11x² + 14x + 5

d)

x³ - 11x² + 14x + 3

17.

Subtract the polynomials.
(3x³ + 3x² + 5) – (x³ – 2x² + x – 4)

a)

4x³ + 5x² + 9

b)

2x³ + 5x² – x + 9

c)

2x³ + 1x – 1x² – 1

d)

2x⁶ +5x⁵ – 1x – 1

18.

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

a)

2x²+ 3x +1

b)

-2x²- 11x -4

c)

2x² + 5x -7

d)

-2x² + 11x -4

19.

Simplify:

a)

-4x - 3

b)

x² - 3

c)

-4x² - 6x

d)

-4x - 6

20.

^{The perimeter of the
triangle is 10x+20. Find the length of the missing side}

a)

6x+10

b)

15x+30

c)

5x+10

d)

5x-10

21.

When the 1st differences are equal, it is a ______ function (a degree of 1).

a)

linear

b)

quadratic

c)

exponential

d)

cubic

22.

What are the 1st differences, and what does it mean about the function?

a)

+8, so it is linear

b)

-8, so it is linear

c)

+2, so it is linear

d)

+8, so it is quadratic

23.

When the 2nd differences are equal, it is a ______ function (a degree of 2).

a)

linear

b)

quadratic

c)

exponential

d)

cubic

24.

Zach was making a table of 1st and 2nd differences for a quadratic function. Where is his mistake?

a)

What are you talking about? There's no mistake!

b)

He messed up on the first-first difference (red one). It should be a positive 2.

c)

He messed up on the second-first difference (blue one). It should be a positive 2.

d)

He messed up on the third-first difference (green one). It should be +4.

25.

Which of the following is the graph of

f\left(x\right)=-\frac{1}{2}\ ^3\sqrt{x}

a)

b)

c)

d)

26.

$f\left(x\right)=\left(x-9\right)^3$

Find the inverse of the given function. (Remember that the x & y switch)

a)

$f^{-1}\left(x\right)=\ ^3\sqrt{x}+9$

b)

$f^{-1}\left(x\right)=\ ^3\sqrt{x}-9$

c)

$f^{-1}\left(x\right)=\ ^3\sqrt{x+9}$

d)

$f^{-1}\left(x\right)=\ ^3\sqrt{x-9}$

27.

Find the inverse of the function:

$f\left(x\right)=\ ^3\sqrt{4x}-5$

a)

$f^{-1}\left(x\right)=-4\left(x+5\right)^3$

b)

$f^{-1}\left(x\right)=\frac{1}{4}\left(x-5\right)^3$

c)

$f^{-1}\left(x\right)=\frac{1}{4}\left(x+5\right)^3$

d)

$f^{-1}\left(x\right)=\left(4x\right)^3+5$

28.

What is the inverse of $y=\left(x-7\right)^3+3$ ?
(Remember the x & y variables switch)

a)

$y^{-1}=\ ^3\sqrt{x-3}+7$

b)

$y^{-1}=\ ^3\sqrt{x+3}+7$

c)

$y^{-1}=\ ^3\sqrt{x-3}-7$

d)

$y^{-1}=\ ^3\sqrt{x+3}-7$

29.

The graph of a function is shown. What are the domain and range of this function?

a)

Domain: (-∞, ∞)
Range: (-∞, 2]

b)

Domain: [2, ∞)
Range: (-∞, ∞)

c)

Domain: (-∞, ∞)
Range: (-∞, ∞)

d)

Domain: (-∞, 2]
Range: [2, ∞)

30.

Describe the transformations:

f(x) = (x + 2)³ - 6

a)

Right 2, Down 6

b)

Left 2, Up 6

c)

Left 2, Down 6

d)

Right 2, Up 6

e)

None

31.

What is the x-intercept of f(x) = ∛(x+1) - 2?

a)

(7, 0)

b)

(-7, 0)

c)

(0, 7)

d)

(0, -7)

e)

None

32.

Solve the cube root equation

a)

-984

b)

984

c)

26

d)

-26

e)

None

33.

Solve the cube root equation

a)

78

b)

-228

c)

228

d)

-78

e)

None

34.

Solve the cube root equation

a)

-125

b)

125

c)

25

d)

-25

e)

None

35.

Solve the cube root equation

a)

36

b)

-216

c)

216

d)

-36

e)

None

36.

What transformations have occurred to get the graph of g(x) from the graph of f(x)?

a)

vertical shrink by a factor of 1/4,translation down 2 units

b)

vertical shrink by a factor of 1/4,translation right 2 units

c)

vertical stretch by a factor of 1/4,translation down 2 units

d)

vertical stretch by a factor of 1/4,translation right 2 units

Test 4 REVIEW: Cubic/Cubed Root & Polynomial Functions

Total questions: 36

Worksheet time: 3hrs 56mins

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