Free Printable Unit 3 Study Guide

1.

List the possible rational zeros of

f(x) = x³ - 4x² -4x + 16

a)

1, 2, 4, 8, 16

b)

$\pm1,\pm2,\pm4,\pm8,\pm16$

c)

$\pm1,\pm4,\pm\frac{1}{4}$

d)

-2 and-4

2.

The degree of the polynomial determines the max number of roots.

a)

True

b)

False

3.

What is another way to say "where a function crosses the x-axis"?

a)

x-intercept

b)

zero

c)

root

d)

all of these.

4.

Select ALL the zeros of the equation.

a)

-7

b)

0

c)

-5

d)

-6

5.

Select ALL the x-intercepts for the equation? $f\left(x\right)\ =\ \left(x-3\right)\left(x+2\right)\left(x+2\right)$

a)

(-3, 0)

b)

-2

c)

(-2, 0)

d)

3

6.

What is the degree of the polynomial function
P(x)=3x⁴-7x²-2x⁷-x+4

a)

4

b)

7

c)

2

d)

11

7.

How many zeros does the polynomial function
P(x) = 3x⁴+4x-8 have?

a)

1

b)

2

c)

3

d)

4

8.

If the binomial (x - 7) is a factor of the polynomial function f(x), which statement must be true?

a)

f(7) = -7

b)

f(7) = 0

c)

f(-7) = 0

d)

f(-7) = -7

9.

Is (x-7) a factor of (x²-5x+14)?

a)

Yes

b)

No

10.

Find all zeros for the polynomial function P(x) = x³ -3x²-5x+15

a)

3, √5

b)

3, √5, -√5

c)

-3, √5, -√5

d)

-3, 5i, -5i

11.

Given that $x=1$ zero of the function $f\left(x\right)=x^3-9x^2+2x+6$ use synthetic division to help you find all of the other zeros. All solutions must be exact - no approximate answers.

a)

$x=4\pm i\sqrt{10}$

b)

$x=4\pm i\sqrt{22}$

c)

$x=4\pm\sqrt{22}$

d)

$x=-4\pm\sqrt{22}$

12.

Use the Fundamental Theorem of Algebra to state the number of zeros/solutions/roots of the polynomial.

a)

A

b)

B

c)

C

d)

D

13.

Use the Rational Root Theorem to list the possible rational zeros.

a)

A

b)

B

c)

C

d)

D

14.

is -3 a POSSIBLE zero of $f\left(x\right)=3x^3+2x^2-5x+2$

a)

no, 3 is not a factor of 3

b)

yes

c)

no, 2 is not a factor of 3

d)

no, 3 is not a factor of 2

15.

Match the graph to the function

a)

f(x)= -x²+3x+2

b)

f(x) = -x³+2

c)

f(x) = x³+2

d)

f(x) = ⅓x⁴-5x²+2

16.

Match the graph to the function

a)

f(x) = -x⁴-x³+5x²-6

b)

f(x) = x⁴+3x²-3x+1

c)

f(x) = -x³+2x²-x-6

d)

f(x) = x⁴+x³+5x²-6

17.

f(x) = 2x³ - 3x² + 4x -10

State the maximum number of turns the graph of f(x) could make.

a)

3

b)

2

c)

1

d)

0

18.

Does this graph have an absolute minimum?

a)

Yes

b)

No

19.

Find the zeros of the polynomial.
f(x) = (x-5)(2x+3)(7x-4)(x+6)

a)

x = 5, (2/3), 6, (7/4)

b)

x= -5, (3/2), (-4/7), 6

c)

x= 5, (-3/2), (4/7), -6

d)

x= 6, 5, -2/3, -4/7

20.

What are the zeros of the function?

a)

4,1

b)

3,1,-2,-5

c)

-3, -1, 2, 5

d)

-2,4

21.

Does this parabola have a minimum or maximum and what is its value?

a)

minimum: 2

b)

maximum: 2

c)

minimum: 5

d)

maximum: 5

22.

Which function has an axis of symmetry of x = 0?

a)

b)

c)

d)

None of the above

23.

Identify the y-intercept

a)

(0, -3)

b)

(3, 0)

c)

(0, 3)

d)

(2, 1)

24.

What are the green dots called?

a)

y-intercepts

b)

maximum

c)

minimum

d)

roots/x-intercepts

25.

What is the range of the function?

a)

[-1, +∞)

b)

(-1,1)

c)

[1.5, +∞)

d)

(-2, 2)

26.

For the pictured polynomial, at which interval is it decreasing?

a)

(-∞, 2)

b)

(-2, 0)

c)

(0, ∞)

d)

(-3, 1)

27.

On the interval of (0, 2) what is happening?

a)

the graph is decreasing

b)

the graph is increasing

c)

the graph remains constant

28.

How would you describe the point at (0,6)?

a)

Relative Minimum

b)

Absolute Minimum

c)

Relative Maximum

d)

Absolute Maximum

29.

What is the end behavior for the graph?

a)

x → ⁻∞, y→ ⁻∞ and

x→ ∞, y→ ⁻∞

b)

x → ⁻∞, y→ ∞ and

x→ ∞, y→ ∞

c)

x → ⁻∞, y→ ⁻∞ and

x→ ∞, y→ ∞

d)

x → ⁻∞, y→ ∞ and

x→ ∞, y→ ⁻∞

30.

What is the end behavior of this graph?

a)

x → ⁻∞, y→ ⁻∞ and

x→ ∞, y→ ⁻∞

b)

x → ⁻∞, y→ ∞ and

x→ ∞, y→ ∞

c)

x → ⁻∞, y→ ⁻∞ and

x→ ∞, y→ ∞

d)

x → ⁻∞, y→ ∞ and

x→ ∞, y→ ⁻∞

31.

Find the decreasing interval

a)

(-1, infinity)

b)

(-infinity, -1)

c)

(-infinity, 4)

d)

(4, infinity)

32.

What is the range of the function?

a)

[-1, +∞)

b)

(-1,1)

c)

[1.5, +∞)

d)

(-2, 2)

33.

Which TWO statements are true?

a)

The function has an x intercept when $x=-1$

b)

The function has an x intercept when $x=0$

c)

The function has a y intercept when $y=0$

d)

The function has a y intercept when $y=2$

34.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

35.

Use the graph to determine the X-intercepts

a)

(-1,0) and (-3,0)

b)

(1,0) and (3,0)

c)

(0,1) and (0,3)

d)

(0,-1) and (0,-3)

36.

What is the decreasing interval on the function shown?

a)

$\left(-\infty,\ 1\right)$

b)

$\left(-\infty,\ 2\right)$

c)

$\left(2,\ \infty\right)$

d)

$\left(1,\ \infty\right)$

37.

Which of the following is the correct equation for the function graphed?

a)

$f\left(x\right)=\left(x-1\right)^{2\ }\left(x+2\right)^{2\ }$

b)

$f\left(x\right)=\left(x+1\right)^2\left(x-2\right)^{2\ }$

c)

$f\left(x\right)=\left(x-1\right)\left(x+2\right)$

d)

$f\left(x\right)=\left(x+1\right)\left(x-2\right)$

38.

What is the degree of the polynomial? $f\left(x\right)=-2x\left(x+3\right)^2\left(x-7\right)\left(x+5\right)^3$

a)

6

b)

7

c)

5

d)

3

39.

What is the degree of the function graphed?

a)

5

b)

1

c)

3

d)

2

40.

What is the degree of the function graphed?

a)

3

b)

5

c)

7

d)

6

41.

Based on the end behavior of the polynomial, what best describes the leading coefficient?

a)

a negative real number

b)

a positive real number

c)

an even real number

d)

an odd real number

42.

Based on the end behavior of the polynomial, what is the degree of the polynomial?

a)

a negative real number

b)

a positive real number

c)

an odd real number

d)

an even real number

43.

Based on the end behavior which option best describes the leading term?

a)

negative coefficient, even degree

b)

negative coefficient, odd degree

c)

negative degree, odd coefficient

d)

negative degree, even coefficient

44.

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

45.

What is the leading coefficient for the polynomial function f(x) = -6x⁴ + x⁸ + 5x² - 2

a)

1

b)

5

c)

-2

d)

-6

46.

For the pictured polynomial, how many relative maximas are there?

a)

1

b)

2

c)

3

d)

4

47.

For the pictured polynomial, how many relative minimas are there?

a)

1

b)

2

c)

3

d)

4

48.

Match the graph to the function based on what you know about degree, the lead coefficient, and end behavior.

a)

f(x)= -x²+3x+2

b)

f(x) = -x³+2

c)

f(x) = x³+2

d)

f(x) = ⅓x⁴-5x²+2

49.

What is the y-intercept?
f(x) = -x⁴ + x³ + 5x² + x + 6

a)

-1

b)

1

c)

5

d)

6

50.

Where is the function positive and where is it negative?

a)

positive (-2,1) and (3,∞) and negative (-∞,-2) and (1,3)

b)

positive (-∞,-1) and (2,∞) and negative (-1,2)

c)

positive (-1,4) and negative (2,-2)

d)

positive (∞,3) and (1,-2) and negative (3,1) and (-2,-∞)

51.

In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

52.

The function shown in the graph is:

a)

even

b)

odd

c)

neither even nor odd

d)

both even and odd

Unit 3 Study Guide

Total questions: 52

Worksheet time: 2hrs 14mins

Similar Resources on Wayground