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Math > Math - Precalculus > Flashcards

Math - Precalculus Flashcards

1
Q

What are the set of numbers?

A

Natural number (counting numbers from 1 to infinity)
Integers (Includes natural numbers, zero and negative natural numbers)
Rational numbers (ratio of integers)
Irrational numbers (cannot be represented as a ratio of integers)
Real numbers (all numbers)

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2
Q

What is the commutative property of addition?

A

The order of the terms doesn’t matter.

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3
Q

What is the associative property of multiplication and addition?

A

You can put parentheses anywhere.

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4
Q

Vertical shifting: How to shift the graph of a function up or down?

A

To shift up, you add a constant (y = x^2 + c)
To shift down, you substract a constant (y = x^2 - c)

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5
Q

Horizontal shifting: How to shift the graph of a function to the left or right?

A

To shift left, you add to x (y = (x + c)^2 )
To shift right, you substract from x (y = (x - c)^2)

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6
Q

Reflecting: How to reflect a graph on the x or y axis?

A

To reflect a function on the x axis: f(x) = -f(x)
To reflect a function on the y axis: f(x) = f(-x)

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7
Q

Vertical stretching: how to stretch the graph of a function?

A

mutiply the function by a constant > 1: 2f(x)

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8
Q

Vertical shrinking: how to shrink a function?

A

mutiply the function by a constant > 0 and < 1: 0.5f(x)

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9
Q

Horizontal stretching: how to stretch a function?

A

multiply x by a constant > 0 and < 1: f(0.5x)

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10
Q

Horizontal shrinking: how to shrink a function?

A

multiply x by a constant > 1: f(2x)

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11
Q

What is an even function?

A

A function whose graph is symmetric at the y axis.
This function statisfies: f(-x) = f(x)

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12
Q

What is an odd function?

A

A function whose graph is symmetric at the origin.
This function satisfies: f(-x) = -f(x)

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13
Q

When do you switch the sign of an inequation?

A

When multiplying or dividing by a negative number.

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14
Q

What is a one to one function?

A

f^-1(f(x)) = x

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15
Q

How to inverse a function?

A

Isolate x in the function so that x = f(y)

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16
Q

What is the formula to find vertexes of a quadratic function?

A

a(x - h)^2 + k

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17
Q

What does it mean if in a(x - h)^2 + k, a < 0?

A

Then f(h) = k is the maximum.

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18
Q

What does it mean if in a(x - h)^2 + k, a > 0?

A

Then f(h) = k is the minimum.

19
Q

What is a rational function?

A

A polynomial function of form f(x) = P(x) / Q (x)

20
Q

What is an asymptote?

A

A line that a function approaches but never reach.

21
Q

What are the 7 properties of log?

A

log_a (A * B) = log_a A + log_b B
log_a (A / B) = log_a A - log_a B
log_B A = log_a A / log_a B
ln = log_e
a^(log_a x) = x
log_a (A^c) = c log_a A
log_c C^x = x

22
Q

Convert a log function into an exponential function log_a X = y

A

x = a^y

23
Q

Convert an exponential function into a log function y = a^x

A

log_a Y = x

24
Q

What is the next simplification of 4 = x^2?

A

|x| = 2

25
Q

What is the number e?

A

THe value that (1 + 1/n)^n approaches as n becomes bigger.

26
Q

What is the equation of a unit circle centered at origin?

A

x^2 + y^2 = 1

27
Q

What is the equation of the radius of a unit circle?

A

(x - h)^2 + (y - k)^2 = r^2

where:
center (h, k)
radius (r)

28
Q

Draw the sin function

A

look sin function image in desktop

29
Q

What is the amplitude and the period of the sin function?

A

amplitude: 1
period: 2Pi

30
Q

What is the domain and range of a sin function?

A

D: |R
R: [-1, 1]

31
Q

What is the amplitude and the period of the cos function?

A

amplitude: 1
period: 2Pi

32
Q

Draw the cos function

A

see image in desktop

33
Q

What is the domain and range of a cos function?

A

D: |R
R: [-1, 1]

34
Q

Draw the tan function

A

see desktop image

35
Q

What is the domain and range of the tan function?

A

D: [-Pi/2, Pi/2]
R: |R

36
Q

What is the period of a tan function?

A

Pi

37
Q

Define the formula of the sin function in relation to the unit circle

A

sin t = y

38
Q

Define the formula of the cos function in relation to the unit circle

A

cos t = x

39
Q

Define the formula of the tan function in relation to the unit circle

A

tan t = y / x

40
Q

Define the formula of the csc function in relation to the unit circle

A

csc t = 1 / y (0 != y)

41
Q

Define the formula of the sec function in relation to the unit circle

A

sec t = 1 / x (0 != x)

42
Q

Define the formula of the cot function in relation to the unit circle

A

cot t = x / y (0 != y)

43
Q

Factor this: 2t^2 + 7t + 3

A

= 2t^2 + t + 6t + 3
= t(2t + 1) + 3(2t + 1)

because:
2 + 3 = 6 * 1
7 = 6 + 1

Math (3 decks)

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