Things I Should Know Before I Get to Calculus Class

Question 1

Quadratic Formula

Answer 1

Question 2

Slope-intercept Form

Answer 2

y = mx + b

Question 3

Point-slope Form

Answer 3

y - y₁ = m(x - x₁)

Question 4

Vertical Line

Answer 4

x = a

Question 5

Horizontal Line

Answer 5

y = b

Question 6

|x| if x ≥ 0

Answer 6

x

Question 7

|x| if x < 0

Answer 7

-x

Question 8

Symmetry about the y-axis

Answer 8

f(-x) = f(x)

Question 9

Symmetry about the x-axis

Answer 9

f(-x) = -f(x)

Question 10

Symmetry about the origin

Answer 10

f(-x, -y) = f(x, y)

Question 11

Even Function

Answer 11

Symmetric about the y-axis

Question 12

Odd Function

Answer 12

Symmetric about the origin

Question 13

If a function passes the horizontal line test, it…

Answer 13

has an inverse.

Question 14

How do you find the inverse of a function?

Answer 14

Interchange x and y and solve for y.

Question 15

Zeros of a Function

Answer 15

x-intercepts

Question 16

Horizontal Asymptote

Answer 16

OR see horizontal asymptote rules

Question 17

Describe the horizontal asymptote when the higher exponent is on top.

Answer 17

No horizontal asymptote

Question 18

Describe the horizontal asymptote when the higher exponent is on bottom.

Answer 18

y = 0

Question 19

Describe the horizontal asymptote when the exponents are the same.

Answer 19

y = the ratio of the coefficients

Question 20

How do you find the vertical asymptotes of a rational function?

Answer 20

The zeros of the denominator (providing that the rational is irreducible)

Question 21

How do you find the holes of a rational function?

Answer 21

Matching zeroes of the numerator and denominator

Question 22

Describe the following translation.

f(x - h)

Answer 22

f(x) shifts h units right

Question 23

Describe the following translation.

f(x + h)

Answer 23

f(x) shifts h units left

Question 24

Describe the following translation.

f(x) + k

Answer 24

f(x) shifts k units up

Question 25

Describe the following translation.

f(x) - k

Answer 25

f(x) shifts k units down

Question 26

Is [,] closed or open?

Answer 26

Closed

Question 27

Is ( , ) closed or open?

Answer 27

Open

Question 28

Which type of interval contains the endpoints?

Answer 28

Closed

Question 29

Which type of interval does not contain the endpoints?

Answer 29

Open

Question 30

Give the formula for the volume of a rectangular box.

Answer 30

V = lwh

Question 31

Give the formula for the volume of a cylinder.

Answer 31

V = πr²h

Question 32

Give the formula for the volume of a cone.

Answer 32

V = (1/3)πr²h

Question 33

Give the formula for the volume of a sphere.

Answer 33

V = (4/3)πr³

Question 34

Give the formula for the surface area of a sphere?

Answer 34

A = 4πr²

Question 35

Give the formula for the surface area of a cylinder with a top.

Answer 35

A = 2πr² + 2πrh

Question 36

Give the formula for the surface area of a cylinder with an open top.

Answer 36

A = πr² + 2πrh

Question 37

Give the formula for the surface area of a box with a top.

Answer 37

Area of the sides + area of the top and bottom

Question 38

f(x) = a sin [(2π/b) (x - c)] + d

What is the amplitude?

Answer 38

|a|

Question 39

f(x) = a sin [(2π/b) (x - c)] + d

What is the period?

Answer 39

|b|

Question 40

f(x) = a sin [(2π/b) (x - c)] + d

What is the horizontal shift?

Answer 40

c

Question 41

f(x) = a sin [(2π/b) (x - c)] + d

What is the vertical shift?

Answer 41

d

Question 42

What is the domain of y = ln(x)?

Answer 42

All positive reals

Question 43

What is the range of y = ln(x)?

Answer 43

All real numbers (ARN)

Question 44

Is y = ln(x) continuous?

Answer 44

Yes

Question 45

Is y = ln(x) concave up or down?

Answer 45

Down

Question 46

What is the inverse of y = ln(x)?

Answer 46

y = e^x

Question 47

ln 1

Answer 47

0

Question 48

ln e

Answer 48

1

Question 49

ln(ab)

Answer 49

ln(a) + ln(b)

Question 50

ln(a/b)

Answer 50

ln(a) - ln(b)

Question 51

ln aⁿ

Answer 51

n ln a

Question 52

Is y = ln(x) one-to-one?

Answer 52

Yes

Question 53

Define one-to-one.

Answer 53

Each input has only one output and vice versa. (For every x there is one y, and for every y there is one x.)

Question 54

What is the domain of y = e^x?

Answer 54

All real numbers (ARN)

Question 55

What is the range of y = e^x​?

Answer 55

All positive reals

Question 56

Is y = e^x continuous?

Answer 56

Yes

Question 57

y = e^x is always (increasing or decreasing).

Answer 57

Increasing

Question 58

Is y = e^x one-to-one?

Answer 58

Yes

Question 59

What is the inverse of y = e^x?

Answer 59

y = ln(x)

Question 60

e

Answer 60

Question 61

Answer 61

e

Question 62

ln eⁿ

Answer 62

n

Question 63

n ln e

Answer 63

n

Question 64

Solve y = e^x for x.

Answer 64

x = ln y

Question 65

ln e^x

Answer 65

x

Question 66

e^{ln x}

Answer 66

x

Question 67

(e^x)(e^x)

Answer 67

e^2x

Question 68

e^-x

Answer 68

1/e^x

Question 69

e^{x ln a}

Answer 69

a^x

Question 70

Give the formula for exponential growth and decay.

Answer 70

A = Ce^kt

Question 71

Answer 71

0

Question 72

tan x

Answer 72

(sin x)/(cos x)

Question 73

cot x

Answer 73

(cos x)/(sin x)

Question 74

sec x

Answer 74

1/(cos x)

Question 75

csc x

Answer 75

1/(sin x)

Question 76

sin² x + cos² x

Answer 76

1

Question 77

1 + tan² x

Answer 77

sec² x

Question 78

1 + cot² x

Answer 78

csc² x

Question 79

sin (x + y)

Answer 79

sin x cos y + cos x sin y

Question 80

sin (x - y)

Answer 80

sin x cos y - cos x sin y

Question 81

cos (x + y)

Answer 81

cos x cos y - sin x sin y

Question 82

cos (x - y)

Answer 82

cos x cos y + sin x sin y

Question 83

sin 2x

Answer 83

2 sin x cos x

Question 84

cos 2x

Answer 84

cos²(x) - sin²(x)

or

2 cos²(x) - 1

or

1 - 2 sin²(x)

Question 85

cos² x

Answer 85

(1 + cos 2x)/2

Question 86

sin² x

Answer 86

(1 - cos 2x)/2

Question 87

sin (-x)

Answer 87

-sin x

Question 88

cos (-x)

Answer 88

cos x

Question 89

cos 0

Answer 89

1

Question 90

sin 0

Answer 90

0

Question 91

cos (π/6)

Answer 91

Question 92

sin (π/6)

Answer 92

1/2

Question 93

cos (π/4)

Answer 93

Question 94

sin (π/4)

Answer 94

Question 95

cos (π/3)

Answer 95

1/2

Question 96

sin (π/3)

Answer 96

Question 97

cos (π/2)

Answer 97

0

Question 98

sin (π/2)

Answer 98

1

Question 99

cos π

Answer 99

-1

Question 100

sin π

Answer 100

0

Question 101

cos (3π/2)

Answer 101

0

Question 102

sin (3π/2)

Answer 102

-1

Question 103

cos 30°

Answer 103

Question 104

sin 30°

Answer 104

1/2

Question 105

cos 45°

Answer 105

Question 106

sin 45°

Answer 106

Question 107

cos 60°

Answer 107

1/2

Question 108

sin 60°

Answer 108

Question 109

cos 90°

Answer 109

0

Question 110

sin 90°

Answer 110

1

Question 111

cos 180°

Answer 111

-1

Question 112

sin 180°

Answer 112

0

Question 113

cos 270°

Answer 113

0

Question 114

sin 270°

Answer 114

-1

Question 115

Convert 0 radians to degrees.

Answer 115

0°

Question 116

Convert π/6 radians to degrees.

Answer 116

30°

Question 117

Convert π/4 radians to degrees.

Answer 117

45°

Question 118

Convert π/3 radians to degrees.

Answer 118

60°

Question 119

Convert π/2 radians to degrees.

Answer 119

90°

Question 120

Convert π radians to degrees.

Answer 120

180°

Question 121

Convert 3π/2 radians to degrees.

Answer 121

270°

Question 122

Convert 0° to radians.

Answer 122

0

Question 123

Convert 30° to radians.

Answer 123

π/6

Question 124

Convert 45° to radians.

Answer 124

π/4

Question 125

Convert 60° to radians.

Answer 125

π/3

Question 126

Convert 90° to radians.

Answer 126

π/2

Question 127

Convert 180° to radians.

Answer 127

π

Question 128

Convert 270° to radians.

Answer 128

3π/2