Free Printable Level Precal Unit 2 Review Mixed Practice

1.

How many zeros are shown in the picture?

a)

0

b)

1

c)

2

d)

3

2.

How many zeros does the polynomial function $f\left(x\right)=x^4-13x^{2\ }-36$ have?

a)

2

b)

3

c)

4

d)

6

3.

Which root has a multiplicity of 2?

a)

-1

b)

2

c)

4

d)

-4

4.

Which zero will "bounce" off (where you see tangent line) of the x-axis for x(x - 1)²(x + 2)(x + 3)

a)

-1

b)

1

c)

-2

d)

-3

5.

What are the
zeros of the polynomial
y = 3(x + 4)(x + 1)(x - 3)?

a)

-4, -1, 3

b)

3, -3, 4, 1

c)

4, 1, -3

d)

3, -4, -1, 3

6.

Which one of these is NOT a zero of $f\left(x\right)=x^2\left(x-1\right)^2\left(x+5\right)$ ?

a)

0

b)

1

c)

-5

d)

-1

7.

What are the zeros of the polynomial?

a)

X=5, x=-3(multiplicity of 2)

b)

x=-3, x=5(multiplicity of 2)

c)

x=3, x=-5

d)

x=5

8.

What are the x-intercepts of

y= x²- 9x + 14 ?

a)

(-7,0) and (-2,0)

b)

(7,0) and (-2,0)

c)

(7,0) and (2,0)

d)

(9,0) and (-14,0)

9.

Let f(x) = $4x^2-33x-27$ Is x = 9 a zero of the function?

a)

yes

b)

no

10.

Find all zeros: x³ + 3x² = 6x + 8

a)

-4, -1, 2

b)

-4, -1, ±√2

c)

1, 2, 4

d)

4,-1,√2

11.

One zero of 4x³-17x²-150x-189 is 9.
What are other zeros? Select TWO correct answers

a)

4

b)

-1.75

c)

-3

d)

-6

12.

Given x=2 is a zero of h(x).

What are all the zeros of the polynomial h(x)?

a)

$x=-5,\ x=0,\ x=2$

b)

$x=-5\left(multi:2\right)\ x=0,\ x=2$

c)

$x=-5,\ x=0,\ x=2\ \left(multi:2\right)$

d)

$x=5,\ x=0,\ x=-2\left(multi:2\right)$

13.

Which is a list of all zeros of $x^3+7x^2+18x=10x+16$

a)

$x=-4\ and\ x=1$

b)

$x=4,\ x=-1$

c)

$x=-4,\ x=1\ \left(multi:2\right)$

d)

$x=-4\left(multi:2\right)\ x=1$

14.

Given one of the zero is -2, which of the following is the correct factors of polynomial $x^3+x^2-10x+8$

a)

$\left(x-4\right)\left(x+1\right)\left(x+2\right)$

b)

$\left(x-4\right)\left(x+1\right)$

c)

$\left(x+4\right)\left(x-1\right)\left(x-2\right)$

d)

$\left(x-1\right)\left(x-2\right)$

15.

Which of the following are correct factors of the polynomial $f\left(x\right)$

a)

$f\left(x\right)=\left(x-5\right)\left(x-2\right)\left(x+4\right)$

b)

$f\left(x\right)=\left(x-5\right)\left(x+4\right)$

c)

$f\left(x\right)=\left(x+5\right)\left(x+2\right)\left(x-4\right)$

d)

$f\left(x\right)=\left(x+5\right)\left(x+2\right)^{2\ }\left(x-4\right)$

16.

Which is the following is NOT a factor of the polynomial shown in the graph?

a)

(x+1)

b)

(x-2)

c)

(x-4)

d)

(x-1)

17.

Which of the following is NOT a factor of $x^4+3x^3-3x^2-11x-6$

a)

$\left(x-2\right)$

b)

$\left(x+4\right)$

c)

$\left(x+3\right)$

d)

$\left(x+1\right)$

18.

Identify the x-intercepts and write an equation.

a)

$x=-3,\ x=1;\ f\left(x\right)=\left(x+3\right)^2\left(x-1\right)$

b)

$x=3,\ x=-1;\ f\left(x\right)=\left(x-3\right)^2\left(x+1\right)$

c)

$x=-3,\ x=1;\ f\left(x\right)=-\left(x+3\right)\left(x-1\right)^2$

d)

$x=-3,\ x=1;\ f\left(x\right)=-\left(x+3\right)^2\left(x-1\right)$

19.

Which of the following function best describes the graph?

a)

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

b)

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

c)

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

d)

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

20.

Which of the following could be a possible equation for the function shown?

a)

f(x) =(x-3)(x-1)(x+2)

b)

f(x)=(x+3)(x+1)(x-2)

c)

f(x) = -(x-3)(x-1)(x+2)

d)

f(x) = -(x+3)(x+1)(x-2)

21.

Which of the following graph best represents the polynomial function:

$f\left(x\right)=a\left(x-b\right)\left(x-c\right)\left(x-d\right).\ where\ a<0,\ a\ne b\ne c$

a)

b)

c)

d)

22.

Given polynomial function $f\left(x\right)=a\left(x-b\right)\left(x-c\right)\left(x-d\right)\left(x-e\right),\ where\ a>0,\ a=b\ne c\ne d$

a)

b)

c)

d)

23.

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

24.

Which of the following notations are correct for the end behavior of the polynomial? Select TWO correct answers

a)

$x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$

b)

$x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$

c)

$x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

d)

$x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$

25.

Which of the following statement is true for the end behaviors of the polynomial? What is the end behavior as x → -∞ f(x)→ ?

a)

x → -∞ f(x)→∞

x → ∞ f(x)→∞

b)

x → -∞ f(x)→-∞

x → ∞ f(x)→-∞

c)

x → -∞ f(x)→∞

x → ∞ f(x)→-∞

d)

x → -∞ f(x)→-∞

x → ∞ f(x)→∞

26.

What is the range of the function?

a)

[-1, +∞)

b)

(-1,1)

c)

[1.5, +∞)

d)

(-2, 2)

27.

The domain of a polynomial function is always (-∞, +∞).

a)

True

b)

False

28.

For the pictured polynomial, at which intervals is it increasing? Select TWO correct answers.

a)

(-1.61, -0.47)

b)

(-0.47, 1.33)

c)

(1.33, ∞)

d)

$\left(-\infty,-1.61\right)$

e)

(-0.94, 6.91)

29.

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

a)

(-∞, 2)

b)

(-2, 0)

c)

(0, ∞)

d)

(-3, 1)

30.

For the pictured polynomial, which of the following are the relative minimums? Select ALL correct answers.

a)

(3, -2)

b)

(0, 3)

c)

(2, 0)

d)

(4, 1)

e)

(-3, -2)

31.

For the pictured polynomial, which is NOT a relative maximum?

a)

(-5, 1)

b)

(0, 3)

c)

(2, 0)

d)

(4, 1)

32.

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

a)

the graph is decreasing

b)

the graph is increasing

c)

the graph remains constant

33.

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

a)

Relative Minimum

b)

Absolute Minimum

c)

Relative Maximum

d)

Absolute Maximum

34.

Which statement correctly describes a function with EVEN symmetry ?

a)

An EVEN function is symmetric with respect to the x-axis.

b)

An EVEN function is symmetric with respect to the y-axis.

c)

An EVEN function is symmetric with respect to the origin.

d)

An EVEN function is symmetric with respect to the line y = x.

35.

A function g(x) is an ODD function. If g(-3) = 4, which other point lies on the graph g(x)?

a)

(3 , -4)

b)

(-3 , -4)

c)

(4 , -3)

d)

(-4 , 3)

36.

A function f(x) is an EVEN function. If f(4) = 2, which other point lies on the graph of f(x)?

a)

(4 , -2)

b)

(-4 , 2)

c)

(-4 , -2)

d)

(-2 , -4)

37.

Which of the following statements are true about the polynomial function shown in the graph? Choose TWO correct answers

a)

Domain: (-4, 4)

b)

Range: $\left(-\infty,\infty\right)$

c)

Function has two relative maximums

d)

Function is ONLY increasing on interval (-0.2, 2.2)

e)

Function has no vertical or horizontal asymptotes

38.

Which of the following statements are true for polynomial $f\left(x\right)=-x^5+4x^3+4x$ Select THREE correct answers

a)

Domain: (-3, 3)

b)

Range: $\left(-\infty,\ \infty\right)$

c)

f(x) is ONLY decreasing on interval $\left(-\infty,-1.6\right)$

d)

f(x) is increasing on interval (-1.6, 1.6)

e)

f(x) has odd symmetry

39.

Given the graph of an ODD degree polynomial function with a negative leading coefficient, Which of the following statement is true?

a)

The left and right ends of the graph will both lead to negative infinity.

b)

The function is symmetric along origin

c)

The left end of the graph will lead to positive infinity.

40.

Given the graph of an EVEN degree polynomial function with a POSITIVE leading coefficient, Which of the following statement is true?

a)

The right end of the graph will lead to negative infinity.

b)

The function is symmetric along y-axis

c)

The left and right ends of the graph will both lead to positive infinity.

d)

The function will intersect will x-axis at least once

41.

Which of the following statements are true about the symmetry of the polynomial: $f\left(x\right)=3x^5-4x^3+x$ Select TWO correct answers.

a)

Notation: $f\left(x\right)=f\left(-x\right)$

b)

Notation: $f\left(x\right)=-f\left(-x\right)$

c)

Reflection symmetry along y-xis

d)

Rotational symmetry along origin

e)

no symmetry

42.

Which of the following statements are true about the polynomial function:

$f\left(x\right)=-5x^4+3x^2-8$ Select TWO correct answers.

a)

Notation: $f\left(x\right)=f\left(-x\right)$

b)

Notation: $f\left(x\right)=-f\left(x\right)$

c)

Notation: $f\left(x\right)=-f\left(-x\right)$

d)

reflectional symmetry along y-axis

e)

Rotational symmetry along origin

43.

Which of following of the solution of inequality:

$-\left(x-4\right)\left(x+1\right)\left(x-2\right)<0$

a)

$\left(-\infty,\ -1\right)\ and\ \left(2,\ 4\right)$

b)

$\left(-\infty,-1\right]\ and\ \left[2,\ 4\right]$

c)

$\left(-1,\ 2\right)\ and\ \left(4,\ \infty\right)$

d)

$\left[-1,\ 2\right]\ and\ \left[4,\ \infty\right]$

44.

$k\left(x\right)=x^3+4x^{2\ }and\ h\left(x\right)=11x+30$ Find the solution of $k\left(x\right)>h\left(x\right)$

a)

$\left(-\infty,\ -5\right)and\left(-2,\ 6\right)$

b)

$\left(-5,\ -2\right)\ and\ \left(3,\ \infty\right)$

c)

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

d)

$\left(3,\ \infty\right)$

e)

$\left[-5,\ -2\right]\ and\ \left[3,\ \infty\right)$

45.

Find the solution of the inequality: $x^4+x^{3\ }\ge16x^2-20x$

a)

$\left(-\infty,0\right]$

b)

$\left(-\infty,\ -5\right]\ and\ \left[0,\ 5\right]$

c)

$\left[-5,\ \infty\right)$

d)

$\left(-\infty,\ -5\right)\ and\ \left(0,\ \infty\right)$

e)

$\left(-\infty,\ -5\right]\ and\ \left[0,\ \infty\right)$

46.

$f\left(x\right)=x^3+3x^{2\ \ }and\ g\left(x\right)=18x+40$ . What is the solution when $f\left(x\right)\le g\left(x\right)?$

a)

$\left(-\infty,\ -5\right]\ and\ \left[-2,\ 4\right]$

b)

$\left[-5,\ -3\right]\ and\ \left[4,\ \infty\right)$

c)

$\left(-\infty,\ 4\right)$

d)

$\left(-\infty,\ -5\right)\ and\ \left[-2,\ 4\right]$

e)

$\left[-2,\ 4\right]$

Level Precal Unit 2 Review Mixed Practice

Total questions: 46

Worksheet time: 3hrs 34mins

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