Free Printable College Algebra CH 3 REV

1.

Identify the vertex and intercepts of the graph of the equation:
f(x) = (x + 3)² − 2

a)

Vertex: (−3, −2); y-intercept: (0, 7); x-intercepts: (−3±√2, 0)

b)

Vertex: (3, 2); y-intercept: (0, 1); x-intercepts: (±3, 0)

c)

Vertex: (2, −3); y-intercept: (0, 4); x-intercepts: (−2±√3, 0)

d)

Vertex: (−3, −2); y-intercept: (0, −2); x-intercepts: (−3, 0), (−7, 0)

2.

Determine the end behavior of the graph of the function. f(x) = 1/2x³ − 2x

a)

down/up

b)

up/up

c)

down/down

d)

up/down

3.

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

4.

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

5.

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

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

6.

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

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

7.

Describe the end behavior of the graph.

a)

x → -∞, f(x) → ∞ and x→∞, f(x) →⁻∞

b)

x → -∞, f(x) → ∞ and x→∞, f(x) →∞

c)

x → -∞, f(x) → ∞ and x→∞, f(x) → 0

d)

x → -∞,f(x) → -∞and x→ ∞, f(x) → ∞

8.

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→⁻∞

9.

Which function has this end behavior?
Note: f(x)=y

a)

-x²-3x+1

b)

-x³+2x²+3

c)

x⁴+3x³-4x+1

d)

x⁵-4x⁴+2x²-1

10.

Which function has this end behavior?

a)

-1x⁴-3x³+3

b)

-2x⁷+2x⁴+4

c)

3x⁸+3x⁵-4x+7

d)

4x⁵-4x⁴+2x³-9

11.

Find the horizontal asymptote.

a)

y = -2

b)

none

c)

y = 0

d)

y = 1/2

12.

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

13.

When finding the Horizontal asymptotes of a function, you should be thinking...

a)

"Set Bottom = to Zero"

b)

"Top = 0"

c)

"f(0)"

d)

"Look at the Degree of the top and bottom..."

14.

Find the Vertical Asymptotes

a)

x= 0, -2

b)

x= 2

c)

x= -3, 2

d)

x = -3,1

15.

This graph would have...

a)

HA @ y = 1/2

b)

HA @ y = 2

c)

HA @ y = 0

d)

No HA or OA

16.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1

d)

y = 9

17.

Find f(2) if f(x)= 3x-9

a)

0

b)

2

c)

3

d)

-3

18.

Which one means the function goes up on the left

a)

x →-∞, y→∞

b)

x →-∞, y→-∞

19.

Which one means the function goes down on the left

a)

x →-∞, y→∞

b)

x →-∞, y→-∞

20.

What is the RANGE of the function?

a)

(-∞, +∞)

b)

(-∞, 4]

c)

(-∞, 4)

d)

[0, 4]

21.

Given the function g(x) = 2x⁴ - x³ + 8/x which of the intervals must contain a zero?

a)

[-1,1]

b)

[0,2]

c)

[2,4]

d)

None of these intervals

22.

Given the function $f\left(x\right)=x^3+x-3$ , which of the intervals below contains a zero?

a)

[-1,1]

b)

[0,1]

c)

[1,2]

d)

None of these intervals

23.

True or false:

If $f$ is continuous on [-1,1], $f\left(-1\right)=4$

and $f\left(1\right)=-2$ , then there is a zero between -1 and 1.

a)

TRUE

b)

FALSE

c)

CANNOT BE DETERMINED

24.

What is the remainder when x⁴ - 5 is divided by x + 3?

a)

76

b)

81

c)

7

25.

If f(x) = 5x² ─ 7x ─10, find the value of f (5) using synthetic division.

a)

150

b)

80

c)

70

26.

Given P(x) = x³ + x² – x ─ 9, what is the value of P (4)?

a)

14

b)

-53

c)

67

27.

The expression x³ ─ kx² +2x +5 leaves a remainder of 2 when divided by x ─ 3. Find the value of k.

a)

4

b)

-4

c)

8

28.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x-12

b)

2x⁴-x³-25x²-12x+0

29.

(2x³ - 5x² + 3x + 7) ÷ (x - 2)

a)

2x³ - x² + x + 9

b)

2x² - x + 1

c)

2x² - x + 1 + 9/x-2

d)

2x² - 9x - 15 - 23/x-2

30.

Is (x-4) a factor of (x³ +x² -16x-16)?

a)

YES

b)

NO

31.

What is the Y-INTERCEPT?
$f(x)=-3(x+1)^2-5$

a)

(0, -8)

b)

(0, -5)

c)

(0, -3)

d)

(0, -1)

32.

What is the vertex for the parabola?
$f(x)=4(x-2)^2+3$

a)

(-2, 3)

b)

(2, -3)

c)

(4, 3)

d)

(2, 3)

33.

What is the vertex of the following parabola?
$y=3(x+5)^2-4$

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

34.

What is the axis of symmetry of the parabola?
$f(x)=\frac{1}{2}(x-4)^2+3$

a)

x = 4

b)

x = -4

c)

x = 1/2

d)

x = 3

35.

Find the ZEROS of the function:

$y=\frac{1}{2}\left(x+4\right)^2-8$

a)

x = 4, x = -12

b)

x = 0, x = -8

c)

x = 4, x = -4

d)

x = 1, x = 2

36.

Find the Y-INTERCEPT of the function:

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

a)

(0, 102)

b)

(0, -48)

c)

(0, -5)

d)

(0, 2)

37.

A parabola has a vertex at (1,6) and passes through (3,-18). Write the equation in vertex form.

Formula: f(x) = a(x - h)²+ k

a)

f(x) = 3(x - 1)²- 18

b)

f(x) = -6(x - 1)²+ 6

c)

f(x) = 6(x - 3)²- 18

d)

f(x) = -3(x + 1)²- 6

38.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

39.

Identify the vertex and whether the graph opens up or down.

a)

(5, 2); opens up

b)

(5, 2); opens down

c)

(-5, 2); opens up

d)

(-5, 2); opens down

40.

Which formula do you use to find the x-value of the vertex?

a)

b)

c)

d)

41.

Which root has even multiplicity?

a)

1

b)

-4

c)

-1

d)

2

42.

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)

43.

What is the Degree of this polynomial:
f(x)= x³(x + 3)²(x – 5)

a)

Degree: 6

b)

Degree: 5

c)

Degree: 3

d)

Degree: 2

44.

What could be the function for this graph in factored form?

a)

f(x) = (x-4)²(x+2)

b)

f(x) = (x+4)²(x-2)

c)

f(x) = (x-4)(x+2)²

d)

f(x) = (x+4)(x-2)²

45.

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

46.

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

a)

1

b)

2

c)

3

d)

4

47.

Determine the y-intercept
f(x) = x³ - 5x² - 25x + 125

a)

(0,0)

b)

(0,25)

c)

(0,125)

d)

(0,5)

48.

Which one of these are not a zero of $f\left(x\right)=-2x\left(3x+1\right)^2\left(x+7\right)^7$

a)

-2

b)

0

c)

$-\frac{1}{3}$

d)

-7

49.

What is the multiplicity of the zero x=-5 for the function $f\left(x\right)=x^2\left(x-1\right)^4\left(x+5\right)$ ?

a)

1

b)

2

c)

3

d)

4

50.

Which polynomial has this type of end behavior?

a)

$-x^2(x-1)(x+2)$

b)

$-3x^3(x-2)^2$

c)

$-x^2(-x+2)^3$

d)

$x^4\left(3x-12\right)^2$

College Algebra CH 3 REV

Total questions: 50

Worksheet time: 4hrs 10mins

Similar Resources on Wayground