Free Printable RF1 Final

1.

When finding the inverse of a relation,
1st you replace f(x) with y
2nd switch the x's and y's
What do you do next?

a)

solve for y

b)

replace y with f^-1(x)

c)

solve for x

d)

find the greatest common factor

2.

Find the inverse for $y=x^2-1$

a)

$y=-x+1$

b)

$y=2x+1$

c)

$y=\sqrt{x}+1$

d)

$y=\sqrt{x+1}$

3.

Find the inverse of $f\left(x\right)=\sqrt{x}+8$

a)

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

b)

$f^{-1}\left(x\right)=x^2-8$

c)

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

d)

$f^{-1}\left(x\right)=\left(x-8\right)^2$

4.

Find the function's maximum and minimum points

a)

no maximum

minimum (-4,-1)

b)

no minimum

maximum (-3, 1)

c)

no maximum

minimum (-1,-4)

d)

maximum (-3,1)

minimum (0,-3)

5.

Identify the function's x- and y-intercepts.

a)

x-int (1,0) and y-int (0,-1)

b)

x-int (0,1) and y-int (-1,0)

c)

x-int (1,∞) and y-int (-∞,-1)

d)

x-int none and y-int (-1,1)

6.

What's the name of the inverse of g(x)?

a)

f(x)

b)

f^-1(x)

c)

y

d)

g^-1(x)

7.

What is the first step in finding the equation of the inverse of a function?

a)

get x by itself

b)

switch x and y

c)

solve for y

d)

write the function in inverse function notation

8.

What equation represents the quadratic function?

a)

y = (x - 8)²

b)

y = (x + 8)²

c)

y = x² - 8

d)

y = x² + 8

9.

What equation represents the quadratic function?

a)

y = (x - 4)²

b)

y = (x + 4)²

c)

y = x² - 4

d)

y = x² + 4

10.

What equation represents the quadratic function?

a)

y = (x - 5)² - 3

b)

y = (x - 5)² + 3

c)

y = (x + 5)² - 3

d)

y = (x - 3)² - 5

11.

Describe the transformation of the graph y = (x)³ + 6

a)

Right 6

b)

Left 6

c)

Up 6

d)

Down 6

12.

Describe the transformations of the graph y = (x - 3)³ -2

a)

Right 3, Down 2

b)

Left 3, Up 2

c)

Right 3, Up 2

d)

Left 3, Down 2

13.

If the blue is f(x)=x^2,then the red must be

a)

g(x)=x²-5

b)

g(x)=x²+5

c)

g(x)=(x-5)²

d)

g(x)=(x+5)²

14.

Find the inverse of f(x) = -3x²+5

a)

b)

c)

d)

15.

a)

b)

c)

d)

16.

What is an asymptote?

a)

When the denominator is equal to 0.

b)

When factors in the numerator and denominator cancel.

c)

A line that the function gets close to, but does not touch.

d)

A line that the function intercepts.

17.

$\sqrt{x+13}-8=-2$

a)

87

b)

no solution

c)

23

d)

$\sqrt{10}-13$

18.

What creates a hole in the graph of a rational function?

a)

Crossing the x-axis

b)

An absence of dirt.

c)

Crossing a vertical asymptote.

d)

A factor that cancels out.

19.

Find the coordinates of the hole.

a)

(-3, -3)

b)

(-3, 3)

c)

(3, -3)

d)

(3, 3)

20.

What is the equation of the rational function graphed?

a)

b)

c)

d)

21.

What are the asymptotes?

a)

x = -3 y = 1

b)

x = 3 y = 1

c)

x = -3 y = -1

d)

x = 3 y = -1

22.

What is (j ∘ k)(x)?

a)

$\sqrt[\ ]{\left(9-x\right)+6}$

b)

$9-\sqrt[\ ]{x+6}$

c)

$\sqrt[\ ]{x+6}\left(9-x\right)$

d)

$\sqrt[\ ]{\left(x+6\right)\left(9-x\right)}$

23.

What operation allows us to verify if functions are inverses?

a)

Multiplying

b)

Dividing

c)

Adding

d)

Composing

24.

What is the FIRST step I need to take to solve for x in the following equation?

a)

Add 9 to both sides

b)

Take the square root of both sides

c)

Divide both sides by 49

d)

Multiply both sides by 9

25.

If

f(x) = 2x + 8

Find f(a)

a)

2a + 8

b)

a(2x + 8)

c)

a

d)

ax

26.

Find the slope of the line that passes through the points (2, 4) and (6, 12)

a)

1/2

b)

-1/2

c)

2

d)

-2

27.

f(x) = 2x² + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].

a)

2

b)

1/2

c)

-2

d)

-1/2

28.

Average Rate of Change is also known as...

a)

y-intercept

b)

x-intercept

c)

linear

d)

slope

29.

Is the function Linear or Nonlinear?

a)

Linear

b)

Nonlinear

30.

What does "m" represent in y=mx+b?

a)

y-intercept

b)

slope

c)

macaroni

d)

nothing

31.

What does 'b" represent in y=mx=b

a)

y-intercept

b)

macaroni

c)

nothing

d)

slope

32.

What is the slope in the equation: y=4x+3

a)

3

b)

4x

c)

4

d)

x

33.

What is the y-intercept in the following equation: y=-4x-5

a)

-4

b)

-4x

c)

5

d)

-5

34.

What is the average rate of change of y = 2(3)^x at [2, 4]?

a)

72

b)

3

c)

36.8

d)

630

35.

Which of the following is the correct formula for average rate of change?

a)

$\frac{\Delta x}{\Delta y}$

b)

$\frac{\Delta y}{\Delta x}$

c)

$y=mx+b$

36.

1. Find the average rate of change of the linear polynomial f(x) = 3x - 2 over the interval [1, 4].

a)

2

b)

3

c)

10

d)

5

37.

Find the average rate of change over the given interval.

a)

4

b)

7

c)

7/3

d)

3/7

38.

$96=6\left(k+8\right)$

a)

$12$

b)

$8$

c)

$-4$

d)

$9$

39.

An equation is...

a)

a problem that contains at least one variable and at least one operation; no equal sign

b)

a mathematical sentence showing two expressions are equal.

c)

The solution for a variable

d)

The value that results in a true sentence

40.

Solve:
8w - 8 = -4w + 16

a)

8

b)

16

c)

24

d)

2

41.

10(h+1)-4=76

a)

h=10

b)

h=4

c)

h=7

d)

h=76

42.

The graph of $g\left(x\right)\ =-2\left(x+1\right)^3$ can be obtained from the graph of $f\left(x\right)=x^3$ , the cubic parent function, by applying which of the following transfo1mations?

a)

Horizontal shift 1 unit to the right; horizontal stretch by a factor of 2; reflection over the x-axis

b)

Horizontal shift 1 unit to the right; horizontal compression by a factor of $\frac{1}{2}$ ; reflection over the x-axis

c)

Horizontal shift 1 unit to the left; horizontal stretch by a factor of 2; reflection over the x-axis

d)

Horizontal shift 1 unit to the left; horizontal compression by a factor of $\frac{1}{2}$ ; reflection over the x-axis

43.

If P(3,5) is a point on the graph of y = f (x), identify the corresponding point on the graph of $y=f\left(x-1\right)+7$

a)

(2,12)

b)

(4,-12)

c)

(2.,-2)

d)

(4,12)

44.

Let f and g be the functions defined by f(x) = $x^2+1$ and g(x) = $\sqrt[2]{x-2}$ . Which of the following represents the equation of h(x)= (f o g)(x)?

a)

h(x) = $\sqrt[2]{x^2-1}$

b)

$h\left(x\right)=\sqrt[2]{x^2+1}$

c)

$h\left(x\right)=x-1$

d)

$h\left(x\right)=x+1$

45.

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

a)

S + A = 530
3S + 4A = 1740

b)

S + A = 530
4S + 3A = 1740

c)

S + A = 1740
3S + 4A = 530

d)

S + A = 1740
4S + 3A = 530

46.

Two lines have the following equations:

$4x+3y=7$

$x+2y=-2$

At what point do the intersect?

a)

$\left(1,1\right)$

b)

$\left(0,-1\right)$

c)

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

d)

$\left(6,-4\right)$

47.

Based on the graph of the following system, determine the solution.

a)

$\left(4,2\right)$

b)

$\left(1,4\right)$

c)

$\left(2,4\right)$

d)

no solution

48.

If a system of equations has one solution, what does the graph look like?

a)

intersecting lines

b)

parallel lines

c)

skew lines

d)

same line

49.

Which variable should we eliminate first?

a)

x

b)

y

50.

After we eliminate y, what does x equal?

a)

x = 2

b)

x = 2.8

c)

x = 5

51.

Use x=2 to substitute into the first equation.

a)

2(2) + 2y = -2

b)

2x + 2(2) = -2

52.

What equation does 2(2) + 2y = -2 become?

a)

2 + 2y = -2

b)

4 + 2y = -2

53.

Solve 4 + 2y = -2

a)

y = -1

b)

y = -2

c)

y= -3

54.

Which variable should we eliminate first?

a)

x

b)

y

55.

Which is the standard form for a quadratic equation?

a)

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

b)

$ax^2+bx+c=0$

c)

$y=a\left(x-h\right)^2+k$

d)

$a^2+b^2=c^2$

56.

Which is the quadratic formula?

a)

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

b)

$ax^2+bx+c=0$

c)

$y=a\left(x-h\right)^2+k$

d)

$a^2+b^2=c^2$

57.

Solve using any method:

x²-5x+6=0

a)

{1, -6}

b)

{3, 2}

c)

{-3, 2}

d)

{-1, 6}

58.

Solve using any method:

2x² + 16x = 18

a)

{-1, 9}

b)

{-9, 1}

c)

(2, 18)

d)

{2, 16}

59.

Solve using any method:

2x² - 9x - 35 = 0

a)

$\left\{\frac{7}{2},\ -6\right\}$

b)

$\left\{-\frac{5}{2},\ 5\right\}$

c)

$\left\{\frac{-3}{7},\ 6\right\}$

d)

$\left\{-\frac{5}{2},\ 7\right\}$

60.

What is the vertex of f(x)=5x²- 20x + 3?

a)

V(2, -17)

b)

V(-2, -17)

c)

V(-2, 63)

d)

V(2, 63)

61.

What is the process of solving quadratics by factoring?

a)

Finding two binomials that multiply together to give the quadratic expression and setting each binomial equal to zero to solve for the variable.

b)

Subtracting the quadratic expression from a binomial to find the variable.

c)

Dividing the quadratic expression by a binomial to find the variable.

d)

Finding two trinomials that multiply together to give the quadratic expression and setting each trinomial equal to zero to solve for the variable.

62.

Solve for x:

(x + 6)²= 49

a)

x=7,12

b)

x=±7

c)

x=1,-13

d)

x=43,-55

63.

What should you do first to solve this equation using quadratic formula?

x² + 6x - 13 = 3

a)

Get factored form

b)

Write down: a=1, b=6, c=-13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

64.

When solving a quadratic equation, when do you use the plus or minus (±) symbol?

a)

After taking the square root of both sides

b)

After adding the square to both sides

c)

After taking half of b

d)

After setting the equation equal to zero

65.

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

a)

vertical

b)

horizontal

c)

slant

d)

none

66.

The horizontal asymptote equals zero when:

a)

the degree of the numerator and denominator are equal

b)

the degree of the numerator is less than the degree of the denominator

c)

the degree of the numerator is greater than the degree of the denominator

d)

the numerator equals zero

67.

Increasing or Decreasing?

a)

A

Increasing

b)

B

Decreasing

68.

Classify the following graph.

a)

Exponential Growth

b)

Exponential Decay

c)

Logarithmic

69.

All of the x values or inputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

70.

State whether this function is growth or decay: $y=\frac{3}{4}\left(.95\right)^x$

a)

Growth

b)

Decay

71.

What is the domain and range of the function y=2^x?

Use the graph to help!

a)

Domain: −∞<x<∞

Range: y>0

b)

Domain: −∞<x<∞

Range: y>1

c)

Domain: −2<x<∞

Range: y>0

d)

Domain: −∞<x<∞

Range: y<0

72.

What is the definition of a function?

a)

Has inputs and outputs

b)

Every input has only ONE output

c)

Inputs have different outputs every time

d)

x-values and y-values

73.

Determine the slope and y-intercept from the following equation: y = 3/2x + 3

a)

slope: 5 y-intercept: (0,3)

b)

slope: 3/2 y-intercept: (0,3)

c)

slope: 4 y-intercept: (0,3/2)

d)

slope: 1/5 y-intercept: (0,5)

74.

Write an equation of the line containing (-1,1) and (4,-9).

a)

y=-2x-1

b)

y=1/2x+1

c)

y=2x

75.

What two x-values would have a rate of change of zero? Select all that apply

a)

4 and 7

b)

1 and 8

c)

1 and 2

d)

2 and 8

e)

4 and 2

76.

How else can you write $\sqrt{x}$ ?

a)

$x^{\frac{1}{2}}$

b)

$x^2$

c)

$x^{-2}$

d)

$x^{\frac{1}{4}}$

77.

How else could you write $4^{-2}$ ?

a)

$16$

b)

$-16$

c)

$-\frac{1}{16}$

d)

$\frac{1}{16}$

78.

Which exponential expression is equal to $\sqrt[7]{b}$ ?

a)

$b^{-\frac{1}{7}}$

b)

$\frac{1}{b^7}$

c)

$b^{\frac{1}{7}}$

d)

$b^7$

79.

What is the value of the index?

a)

$\frac{1}{8}$

b)

$8$

c)

$5$

d)

$\frac{5}{8}$

80.

(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

81.

Rewrite the following

∛x⁵

a)

x^3/5

b)

x^5/3

c)

x²

d)

x³⋅x⁵

82.

$\sqrt{ }$ has an imaginary index of ___.

a)

1

b)

0

c)

2

83.

a)

2 / x²

b)

-2x²

c)

2x²

d)

2x¹⁴

84.

(y⁹)^-2

a)

y¹⁸

b)

y¹¹

c)

1/y¹⁸

85.

Rewrite in Exponential Form.

a)

A

b)

B

c)

C

d)

D

86.

Rewrite in radical form.

a)

A

b)

B

c)

C

d)

D

87.

What (if any) holes exist?

a)

x=2

b)

x=2 and x=3

c)

x=-3

d)

x=3

88.

What is the horizontal asymptote?

a)

y = -4

b)

y = 1

c)

x = 1

d)

y = -6

89.

Determine the Limit at Infinity

a)

0

b)

-1

c)

-5/2

d)

DNE

e)

infinity

90.

Find the limit

a)

⁹/₁₂

b)

0

c)

∞

d)

-∞

RF1 Final

Total questions: 90

Worksheet time: 6hrs 19mins

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