Free Printable 012 Fall 22 Review

1.

How do you read f(x)?

a)

f x

b)

f of x

c)

f parenthesis x

d)

f with an x inside parenthesis

2.

What is the definition of a function?

a)

Has inputs and outputs

b)

Inputs have different outputs every time

c)

x-values and

y-values

d)

Every input has only one output

3.

Is this graph a function or not a function?

a)

Function

b)

Non Function

4.

If f(x) = 2x + 1, find f(1).

a)

f(1) = 1

b)

f(1) = 4

c)

f(1) = 0

d)

f(1) = 3

5.

What is f(1)?

a)

1

b)

5

c)

0

d)

4

6.

Find h(5) using the equation.

a)

-25

b)

25

c)

3

d)

7

e)

undefined

7.

Find f(0)

a)

-3

b)

18

c)

4

d)

0

8.

Find the difference quotient for $f\left(x\right)=3x$

a)

$3h$

b)

$3x$

c)

$3$

d)

$3\left(x+h\right)$

9.

Find the difference quotient for $x^2-1$

a)

2x

b)

2x+h

c)

$h^2-1$

d)

$x^2+2xh+h^2-1$

10.

$f\left(x\right)=3x^2+5x-8$

$g\left(x\right)=5x-7$

find (f+g)(3)

a)

34

b)

42

c)

88

d)

27

11.

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

$g\left(x\right)=4x-5$

find (fg)(-1)

a)

-8

b)

-9

c)

72

d)

-72

12.

If $f\left(x\right)=-2x+3$ and $g\left(x\right)=-3x+2,$ find $f\left[g\left(x\right)\right].$

a)

$-x+1$

b)

$-2x^2$

c)

$6x-1$

d)

$5x+7$

13.

If $f\left(x\right)=x^2-1$ and $g\left(x\right)=4x-3,$ find $\left[f\circ g\right]\left(3\right).$

a)

$43$

b)

$91$

c)

$80$

d)

$26$

14.

If $f\left(x\right)=x^2-1$ and $g\left(x\right)=4x-3,$ find $\left[g\circ f\right]\left(x\right).$

a)

$-3x+1$

b)

$4x^2-7$

c)

$-2x^2+3$

d)

$5x^2+6$

15.

The inverse of the function f(x) is written as ...

a)

f ^-1(x)

b)

f ²(x)

c)

f '(x)

d)

f ⁺(x)

16.

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

a)

(1, 4) and (4, 6)

b)

(-4, -1) and (-6, -4)

c)

(-1, -4) and (-4, -6)

d)

(4, 1) and (6, 4)

17.

Find f(g(x)) and g(f(x)) to determine if these are inverse functions.

a)

Inverse Functions

b)

Not Inverse Functions

18.

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

a)

$\frac{x-5}{1}$

b)

$\frac{x}{5}-1$

c)

$x-\frac{1}{5}$

d)

$\frac{x-1}{5}$

19.

Find the inverse of the function $f\left(x\right)=-4x+3$

a)

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

b)

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

c)

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

d)

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

20.

Find the inverse of

$f\left(x\right)=\sqrt[]{x-3}$

a)

$f^{-1}\left(x\right)=x^2+3$

b)

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

c)

$f^{-1}\left(x\right)=\left(x+3\right)^2$

21.

If you were to plot the point (4, -12) what would be the correct method?

a)

Up 4, left 12

b)

Right 4, up 12

c)

Down 4, left 12

d)

Right 4, down 12

22.

^{What is the x- intercept of the line?}

a)

(1, 0)

b)

(2, 0)

c)

( -1, 0)

d)

(-2, 0)

23.

What are the x- and y -intercepts on this graph?

a)

(0,5), (0,5)

b)

(5,0), (5,0)

c)

(5,0), (0,5)

d)

(0,0), (5,0)

24.

Select ALL symmetries displayed in the graph.

a)

symmetry with respect to the x-axis

b)

symmetry with respect to the y-axis

c)

symmetry with respect to the origin

d)

all of the above

e)

none of the above

25.

Write the equation of a circle with center (h,k) and radius r.

a)

x² + y² = r²

b)

(x + h)² + (y + h)² = r²

c)

(x - h)² + (y - k)² = r²

d)

(x - h)² - (h - k)² = r

26.

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

a)

4

b)

2

c)

3

d)

16

27.

In the equation
(x-3)²+(y-2)²=16, the center of the circle is...

a)

(3,2)

b)

(-3, -2)

c)

(-2, -3)

d)

(2, 3)

28.

Write the equation of a circle with center
(7, 0) with radius 3.

a)

(x - 7)² + y² = 9

b)

x² + (y -7)² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

29.

What is the center of the circle with equation x² + y² = 1?

a)

(1, 1)

b)

(0, 0)

c)

not enough information

d)

(-1, -1)

30.

The point (-5,6) is on a circle with center (-1,3) write the equation of the circle

a)

(x+1)² + (y-3)²= 4000

b)

(x+5)² + (y-0)²= 25

c)

(x+1)² + (y-3)²= 25

d)

(x-1)² + (y+3)²= 25

31.

What is the equation for the circle, if it has diameter endpoints at (3,-4) and (-5,-4)?

a)

(x+1)² + (y-4)² = 4

b)

(x+1)² + (y+4)² = 16

c)

(x-1)² + (y-4)² = 16

d)

(x+1)² + (y+4)² = 4

32.

Find the distance between J and K.

a)

√68

b)

√8

c)

9

d)

√53

33.

What is the midpoint between (-4,4)
and (-2,2)?

a)

(3,2)

b)

(-3,3)

c)

(4,5)

d)

(6,7)

34.

Select ALL symmetries displayed in the graph.

a)

symmetry with respect to the x-axis

b)

symmetry with respect to the y-axis

c)

symmetry with respect to the origin

d)

all of the above

e)

none of the above

35.

Use the symmetry tests to determine the type of symmetry for: $y=3x^8-7x^2+2$
i. symmetric with respect to the x-axis
ii. symmetric with respect to the y-axis
iii. symmetric with respect to the origin

a)

i only

b)

ii only

c)

iii only

d)

i, ii, and iii

36.

Use the symmetry tests to determine the type of symmetry for: $x=y^2-4$
i. symmetric with respect to the x-axis
ii. symmetric with respect to the y-axis
iii. symmetric with respect to the origin

a)

i only

b)

ii only

c)

iii only

d)

i, ii, and iii

37.

What is the equation of the circle?

a)

(x+1)² + (y +1)² = 3

b)

(x+1)² + (y -1)² = 3

c)

(x+1)² + (y +1)² = 9

d)

(x-1)² + (y -1)² = 9

38.

Select a point that would be on located on the x axis.

a)

(0,7)

b)

(6,4)

c)

(7,0)

d)

(1,1)

39.

In which quadrant are both numbers negative?

a)

1 (I)

b)

2 (II)

c)

3 (III)

d)

4 (IV)

40.

Which quadrant contains the point named by (2, 5)?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

41.

Which table of values can be defined by y=x+5?

a)

a

b)

b

c)

c

42.

Which graph represents the table?

a)

b)

c)

d)

43.

What ordered pair is a solution of 2y - 3x = 8

a)

(6,13)

b)

(19, 4)

c)

(10,4)

d)

(4,0)

44.

What is 10⁰equivalent to?

a)

1

b)

10

c)

0

d)

100

45.

Evaluate

a)

-1

b)

1/32

c)

-1/32

d)

1

46.

Evaluate when x=3 and y=1

x^{-2}y

a)

9

b)

1/6

c)

1/9

d)

6

47.

Is -4.8 a possible solution for p ≥ -3 ?

a)

Yes

b)

No

48.

When graphing b< 6 would you use an open or closed circle?

a)

open

b)

closed

49.

When graphing an inequality, you use an open dot when you use which symbol?

a)

<, >

b)

≤, ≥

c)

>, ≥

d)

<, ≤

50.

Write the following solution in interval notation:

x ≥ -3

a)

[ -3, ∞ )

b)

( -3, ∞ )

c)

( -∞ , -3 )

d)

( -∞ , -3]

51.

What interval notation does the number line graph represent?

a)

[∞, -5)

b)

(∞, -5)

c)

[-5, ∞)

d)

(-5, ∞)

52.

l - 4 l + l -1 l

a)

5

b)

3

c)

4

d)

-5

53.

What is the value of the expression
x² + y² + x - y
when x = -1 and y = 3

a)

6

b)

8

c)

12

d)

16

54.

8 + (5 + 2) = (8 + 5) + 2 is an example of which property?

a)

Addition Property of Equality

b)

Commutative Property of Addition

c)

Associative Property of Addition

d)

Distributive Property

55.

8 + 1 + 9 = 8 + 9 + 1

a)

Additive Identity Property

b)

Associative Property of Addition

c)

Commutative Property of Multiplication

d)

Commutative Property of Addition

56.

a)

b)

c)

d)

57.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

58.

Simplify (2⁴)(2⁵)

a)

2²⁰

b)

4⁹

c)

4²⁰

d)

2⁹

59.

Write 0.000972 in scientific notation.

a)

9.72 x 10^-4

b)

9.72 x 10^-3

c)

9.72 x 10³

d)

9.72 x 10⁴

60.

Simplify √80

a)

√20 * √4

b)

4√5

c)

√16 * √5

d)

Other

61.

Rationalize the denominator.

$\frac{4}{\sqrt{5}}$

a)

$\frac{4\sqrt{5}}{5}$

b)

$\frac{\sqrt{5}}{4}$

c)

$\frac{\sqrt{6}}{3}$

d)

$\frac{5\sqrt{2}}{2}$

62.

What is the degree of this polynomial?

2x⁴- 3x⁵+ x

a)

-3

b)

2

c)

4

d)

5

63.

Classify by number of terms:
3x³ – 6x

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

64.

What is the coefficient of this term?

9x³

a)

None

b)

9

c)

3

d)

x

65.

Multiply:
(3x – 1)(x + 5)

a)

3x² + 4x + 5

b)

3x² + 4x - 5

c)

3x² + 14x + 5

d)

3x² + 14x - 5

66.

Factor:
10x + 15

a)

100x + 150

b)

10(x + 5)

c)

1(10x + 15)

d)

5(2x + 3)

67.

Factor 4y² – 9.

a)

(2y + 3)(2y – 3)

b)

prime

c)

(2y + 3)(2y + 3)

d)

(2y – 3)(2y – 3)

68.

Factor: x² + 24x + 144

a)

(x + 12)²

b)

(x + 9)²

c)

(x + 15)²

d)

(x + 13)²

69.

Perform the indicated operation.

Write answer in descending order.

( 17x - 8 ) - ( 9x - 27 )

a)

8x - 35

b)

8x + 35

c)

8x + 19

d)

8x - 19

70.

For which value is the expression undefined?

a)

-4

b)

-3

c)

3

d)

0

71.

simplify the expression below:

$\frac{45}{10a-10}$

a)

$\frac{9}{2\left(a-1\right)}$

b)

$\frac{5}{10a}$

c)

$\frac{9}{2\left(1-a\right)}$

d)

$\frac{5}{2\left(a-1\right)}$

72.

Divide the following rational expression:
$\frac{6xy^3}{8ab^2}\div\frac{3x^2y}{4ab^2}=$

a)

$y^2$

b)

$\frac{1}{x}$

c)

$\frac{x^2}{2y}$

d)

$\frac{y^2}{x}$

73.

Simplify the expression:
$\frac{\left(x+10\right)}{3x\left(x+10\right)}=$

a)

$\frac{1}{3x}$

b)

$3x$

c)

$x+10$

d)

$3x^2+30x$

74.

$Simplify:\ \ \frac{x^2+6x}{x^2+3x-18}$

a)

$\frac{x}{x+3}$

b)

$\frac{x}{x-3}$

c)

$\frac{x+6}{x-3}$

d)

$\frac{x}{x+6}$

75.

$\frac{15}{4x}+\frac{5}{4x}$

a)

$\frac{20x}{4}$

b)

$\frac{4}{x}$

c)

$\frac{5}{x}$

d)

$\frac{10}{4x}$

76.

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

a)

$\frac{x\left(5x+6\right)}{\left(x+2\right)\left(x-2\right)}$

b)

$\frac{\left(5x+6\right)}{\left(x+2\right)\left(x-2\right)}$

c)

$\frac{\left(5x^2+6\right)}{\left(x+2\right)\left(x-2\right)}$

d)

$\frac{4x^2+10x}{\left(x+2\right)\left(x-2\right)}$

77.

$\frac{3}{x-3}-\frac{12}{x^2+5x-24}$

a)

$\frac{3\left(x-8\right)}{\left(x+8\right)\left(x-3\right)}$

b)

$\frac{3\left(x-4\right)}{\left(x+8\right)\left(x-3\right)}$

c)

$\frac{\left(3x-8\right)}{\left(x+8\right)\left(x-3\right)}$

d)

$\frac{3\left(x-8\right)}{\left(x^2+5x-24\right)\left(x-3\right)}$

78.

$\frac{3x}{x^2-25}-\frac{2}{x-5}$

a)

$\frac{3x-10}{\left(x+5\right)\left(x-5\right)}$

b)

$\frac{3x-2}{\left(x+5\right)\left(x-5\right)}$

c)

$\frac{x-10}{\left(x+5\right)\left(x-5\right)}$

d)

$\frac{3x^2-2x+10}{\left(x+5\right)\left(x-5\right)}$

79.

Simplify.
$\frac{\frac{1}{x}}{\frac{x-1}{16}}$

a)

$\frac{1}{x}$

b)

$\frac{16x-16}{x^3}$

c)

$\frac{16}{x^2-x}$

d)

$\frac{16}{x^2}$

80.

$\frac{\frac{2x}{x+1}}{\frac{3}{x+1}}$

a)

$\frac{2x\left(x+1\right)}{3}$

b)

$\frac{2x}{3}$

c)

$\frac{3}{2x}$

d)

$\frac{2x\left(x+1\right)}{x+1}$

81.

$\frac{x+\frac{3}{x^2}}{1-\frac{2}{x}}$

a)

$\frac{x^3+3}{x^2-2x}$

b)

$\frac{x\left(x+3\right)}{x-2}$

c)

$\frac{x+3}{x-2}$

d)

$\frac{x\left(x^3+3\right)}{x-2}$

82.

Factor: x³+ 1

a)

(x + 1)³

b)

(x+1)(x²- x + 1)

c)

(x - 1) (x² + x - 1)

d)

(x + 1)(x² - 2x + 1)

83.

Factor this difference of cubes:
x³ - 343

a)

(x + 7) (x² - 7x + 49)

b)

(x² + 1) (x - 343)

c)

(x - 7) (x² + 7x + 49)

d)

(x² - 343) (x + 1)

84.

Solve:
2(2x + 3) = -6(x + 9)

a)

1.2

b)

6

c)

-6

d)

7.5

85.

How would you rewrite the equation after multiplying the LCD?

a)

2x-20=3x+12

b)

2x-5=3x+3

c)

4x-20=6x+12

d)

2x-20=4x+12

86.

The solutions of the quadratic equation
x²-5x+6=0 are

a)

x=1 or x=-6

b)

x=3 or x=2

c)

x=-3 or x= 2

d)

x=-1 or x=6

87.

To complete the perfect square trinomial in the expression x²-22x+_____, we need to add

a)

11

b)

44

c)

121

d)

144

88.

(4 - 2i) - (3 + 6i)

a)

7 - 4i

b)

1 + 4i

c)

1 - 8i

d)

7 - 8i

89.

(2i)(3i)

a)

5i

b)

-5

c)

6i

d)

-6

90.

$Simplify:\ \ \ \ 2i\left(4\ +\ 3i\right)$

a)

$-6\ +\ 8i$

b)

$6\ +\ 8i$

c)

$-6i\ +\ 8i$

d)

$-1\ +\ 8i$

91.

$\left(5-i\right)^2$

a)

15-8i

b)

36

c)

24+10i

d)

24-10i

92.

Find the solution.

8x\ +\ 4\ -10x\ =\ 3\ -\ 9x\ +\ 15

a)

x = 2

b)

x = -1

c)

x = 12

d)

x = 6

93.

What is the y-intercept in the equation x + 2y = 4

a)

(0, 0)

b)

(0, 2)

c)

(4, 0)

d)

(2, 0)

94.

Find the equation of the line that passes through the points:

(2, 2) and (3, 4)

a)

y = 2x + 2

b)

y = -2x - 2

c)

y = -2x + 2

d)

y = 2x - 2

95.

Write the equation of the line with slope 4 through the point (-2, 5).

a)

y = 4x - 13

b)

y = 4x + 13

c)

y = 4x - 3

d)

y = 4x + 3

96.

Write the equation of a line PERPENDICULAR to y = -2x + 1 that passes through the point (2, 3).

a)

$y=-\frac{1}{2}x+\frac{1}{2}$

b)

$y=\frac{1}{2}x+2$

c)

$y=-2x+7$

d)

$y=-2x+8$

97.

Find the slope of the line.

a)

Undefined

b)

0

c)

1

d)

-1

98.

Are these two lines parallel, perpendicular or neither?
y = -1/3x - 5
y = 1/3x + 2

a)

Parallel

b)

Perpendicular

c)

Neither

012 Fall 22 Review

Total questions: 98

Worksheet time: 4hrs 2mins

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