Free Printable Unit 4

1.

Describe the end behavior of the graph.

a)

x → ∞, y→ ∞ and x→∞, y→⁻∞

b)

x → ∞, y→ ∞ and x→⁻∞, y→∞

c)

x → ∞, y→ ∞ and x→⁻∞, y→ 0

d)

x → ∞,y→ ∞and x→ ⁻∞, y→ ⁻∞

2.

What is the equation in factored form of this graph?

a)

f(x) = (x-4)(x-1)²(x+2)(x+4)

b)

f(x) = (x-4)(x+1)²(x+2)(x+4)

c)

f(x) = (x-4)(x-1)²(x-2)(x+4)

d)

f(x) = (x+4)(x+1)²(x-2)(x-4)

3.

How many roots are shown in the picture?

a)

0

b)

1

c)

2

d)

3

4.

How many zeroes are shown in the graph?

a)

1

b)

2

c)

3

d)

4

5.

Which root has a multiplicity of 2?

a)

-1

b)

2

c)

4

d)

-4

6.

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

a)

True

b)

False

7.

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

8.

List the ACTUAL rational zeros of

f(x) = x³ + 7x² - 2x -14 ?

a)

$\pm1,\pm2,\pm7,\pm14$

b)

7, 2

c)

7

d)

- 7

9.

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

10.

How could you determine if x-2 is a factor of 2x³-5x²+x-2?

a)

Use synthetic division and see if the quotient is even

b)

Ask the person sitting next to me

c)

Use synthetic division and see if the remainder is zero

d)

Flip a coin

11.

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

12.

f(x) = 2x³ - 3x² + 4x -10

What is the degree of f(x)?

a)

3

b)

2

c)

1

d)

0

13.

How many roots or zeros does the equation
f(x) = 5x⁴-8x³+4x²-6x+3 have?

a)

3

b)

4

c)

5

d)

0

14.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

a)

Yes, (x-2) is a factor. There is a remainder.

b)

No, (x-2) is not a factor. The remainder is zero.

c)

Yes, (x-2) is a factor. The remainder is zero.

d)

No, (x-2) is not a factor. There is a remainder.

15.

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

16.

If the graph of a function crosses the x-axis, what does that mean about the multiplicity of that zero?

a)

Even

b)

Odd

c)

None

17.

What are the

zeros of the polynomial

y = 5(x + 4)(x + 1)(x - 3)?

a)

-4, -1, 3

b)

3, 5, 4, 1

c)

4, 1, -3

d)

3, -4, -1, 5

18.

What are the zeros of the polynomial function?

y = 3x(x - 6)(x + 5)

a)

0, 6, -5

b)

6, -5

c)

0, -6, 5

d)

3, 6, -5

19.

What are the zeros of the polynomial function?

y = (x + 2)(x - 7)³

a)

-2, 7 multiplicity 3

b)

-2, 7, 3

c)

2, -7 multiplicity 3

d)

2, -7, 3

20.

Odd Multiplicities have which of the following effects on the x-axis?

a)

Cross the x-axis

b)

Tangent to the x-axis

21.

Which equation MOST LIKELY matches the graph?

a)

y = x⁴- x³ + 3x² + 2

b)

y = -x⁴ + x³ + 5x + 2

c)

y = x³ - 2x² + 1x + 3

d)

y = -x³ - 2x² + 1x + 3

22.

What is the degree of the function graphed here?

a)

2

b)

3

c)

4

d)

5

23.

How many real zeros are shown in the graph?

a)

1

b)

2

c)

3

d)

4

24.

Find the choice that is correct

a)

The leading coefficient is 2, the degree is 4

b)

The leading coefficient is 3, the degree is 2

c)

The leading coefficient is 3, the degree is 4

d)

The leading coefficient is 2, the degree is 2.

25.

Find the correct statement about the zeros.

a)

−5 is a zero with multiplicity 1

b)

−5 is a zero with multiplicity 2

c)

−2 is a zero with multiplicity 1

d)

2 is a zero with multiplicity 2

26.

Which function has zeros: x=0, x=5(multiplicity of 3) and x=-6.

a)

f(x) = 9x(x + 5)³(x - 6)

b)

f(x) = 3(x - 5)³(x + 6)

c)

f(x) = -7x(x - 5)³(x + 6)

d)

f(x) = (x - 3)(x - 5)(x + 6)

27.

What are the asymptotes?

a)

$x=-3,\ y=1$

b)

$x=-3,\ y=-1$

c)

$x=1,\ y=-3$

d)

$x=1,\ y=3$

28.

What is the domain and range?

a)

D : All real number x ≠ -3
R: All real number y≠ 1

b)

D : All real number x ≠ 1
R: All real number y≠ -3

c)

D : All real number x ≠ 3
R: All real number y≠ 1

d)

D : All real number x ≠ -1
R: All real number y≠ 3

29.

Find the domain of the function. $f(x)=\frac{x^3}{x+8}$

a)

x cannot equal to 8

b)

x cannot equal to 0

c)

x cannot equal to -8

d)

All real numbers

30.

Find the domain of the function. $f(x)=\frac{x}{2x+4}$

a)

x cannot equal to 2

b)

x cannot equal to 1/2

c)

x cannot equal to -2

d)

All real numbers

31.

What is the horizontal asymptote?

a)

x = 2

b)

x = 7

c)

y = 2

d)

y = 7

32.

Which is the graph of the rational equation:

a)

b)

c)

d)

33.

Which function matches this graph?

a)

$f\left(x\right)=\frac{-4}{x}-2$

b)

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

c)

$f\left(x\right)=\frac{-4}{x-2}$

d)

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

34.

Which functions match this graph?

a)

$f\left(x\right)=\frac{4}{x}+1$

b)

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

c)

$f\left(x\right)=\frac{4}{x+4}$

d)

$f\left(x\right)=\frac{4}{x-4}$

35.

Which asymptote(s) are determined by looking only at the denominator?

a)

vertical

b)

horizontal

c)

both

d)

none

36.

State the Domain and Range.

a)

D: x ≠ 5 , and R: y ≠ 7

b)

D: x ≠ -5 , and R: y ≠ 7

c)

D: x ≠ 5 , and R: y ≠ -7

d)

D: x ≠ 7 , and R: y ≠ 5

37.

What are the asymptotes?

a)

x=-2 and y=-1

b)

x=-2 and y=1

c)

x=2 and y=1

d)

x=2 and y = -1

38.

Select the graph that show the corresponding vertical & horizontal asymptotes to this function

a)

b)

c)

d)

39.

Select the graph that show the corresponding vertical & horizontal asymptotes to this function

a)

b)

c)

d)

40.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 2

d)

y = 4

41.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1

d)

y = 9

42.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1/2

d)

y = 1

43.

What's the vertical asymptote of the function?

a)

x = -9

b)

x = 9

c)

x = 3 , x = -3

d)

x = 3

44.

What's the vertical asymptote of the function?

a)

x = 4

b)

x = 16

c)

x = 4 , x = -4

d)

No vertical asymptote

45.

Select the graph that show the corresponding vertical & horizontal asymptotes to this function

a)

b)

c)

d)

46.

What's the vertical asymptote of the function?

a)

x = 5

b)

x = 0

c)

x =5 , x = -5

d)

x = 25

47.

What are the coordinates of the hole, if one exists.

a)

(-1, -2)

b)

(-1, ½)

c)

(-1, -½)

d)

there isn't one

48.

What are the coordinates of the y-intercept, if one exists.

a)

(0, 0)

b)

(0, 1)

c)

(0, -1)

d)

there isn't one

49.

What is the equation of the slant asymptote?

a)

y = x + 1

b)

y = x + 2

c)

y = x + 3

d)

y = x

50.

What are the x and y intercepts?

a)

(4, 0) and (0, -4)

b)

(-4, 0) and (0, -4)

c)

(-4, 0) and (0, 4)

d)

(0, 0) and (0, -4)

51.

What is the equation of the graph?

a)

b)

c)

d)

52.

Find the y-intercept.

a)

(0, -2)

b)

(0, 2)

c)

(0, 4)

d)

it is undefined

53.

Solve the inequality in interval notation

x^2-9\le0

a)

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

b)

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

c)

$\left[-\infty,-3\right]\cup\left[3,\infty\right]$

d)

$\left[-3,3\right]$

54.

Solve the inequality in interval notation

\frac{x+2}{x-4}\ge3

a)

$\left(-\infty,4\right)\cup\left(7,\infty\right)$

b)

$\left(4,7\right]$

c)

$\left[-\infty,4\right]\cup\left[7,\infty\right]$

d)

$\left[4,7\right)$

55.

Solve the inequality in interval notation

x^2-x-12>0

a)

$\left(-\infty,-3\right)\cup\left(4,\infty\right)$

b)

$\left(-3,4\right)$

c)

$\left[-\infty,-3\right]\cup\left[4,\infty\right]$

d)

$\left[-3,4\right]$

56.

Solve the inequality in interval notation

\frac{5+7x}{1+2x}\ge4

a)

$\left(-\infty,-\frac{1}{2}\right)\cup\left(1,\infty\right)$

b)

$\left(-\frac{1}{2},1\right]$

c)

$\left(-\infty,-\frac{1}{2}\right]\cup\left[1,\infty\right)$

d)

$\left[-\frac{1}{2},1\right)$

57.

Solve the inequality in interval notation

x^3-2x^2-11x+12\ge0

a)

$\left[-3,1\right]\cup\left[4,\infty\right]$

b)

$\left(-3,1\right)\cup\left(4,\infty\right)$

c)

$\left(-3,1\right]\cup\left[4,\infty\right)$

d)

$\left[-3,1\right]\cup\left[4,\infty\right)$

58.

Solve the inequality in interval notation

2x^3+2x^2-4x\le0

a)

$\left[-\infty,-2\right]\cup\left[0,1\right]$

b)

$\left(-\infty,-2\right)\cup\left(0,1\right)$

c)

$\left(-\infty,-2\right]\cup\left[0,1\right]$

d)

$\left(-\infty,-2\right)\cup\left[0,1\right]$

59.

Solve the rational inequality and state your solution in interval notation.

$\frac{x^2-1}{x^2+1}\le0$

a)

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

b)

$\left[-1,\ 1\right]$

c)

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

d)

$\left(-\infty,\ -1\right]\cup\left[1,\ +\infty\right)$

60.

Solve the rational inequality and state your solution in interval notation.

$\frac{x^2+4x-12}{x^2-4x+4}>0$

a)

$\left(-\infty,\ -2\right]\cup\left[6,\ +\infty\right)$

b)

$\left(-\infty,\ -2\right)\cup\left(6,\ +\infty\right)$

c)

$\left(-\infty,\ -6\right]\cup\left[2,\ +\infty\right)$

d)

$\left(-\infty,\ -6\right)\cup\left(2,\ +\infty\right)$

Unit 4

Total questions: 60

Worksheet time: 3600secs

Similar Resources on Wayground