Pre-Requisites Flashcards

1
Q

Slope is a ___ ___ between x and y increments.

A

constant ratio

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2
Q

In a linear equation, equal increments in the ___ ___ correspond to equal increments in the ___ ___.

A

independent variable, dependent variable

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3
Q

Increment

A

Change in a variable

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4
Q

Implied domain

A

When no restrictions are given to a function, the domain is assumed to be the largest set of x-values for which the formula gives real y values.

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5
Q

Even function

A

f(-x) = f(x), symmetric about the y-axis

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6
Q

Odd function

A

f(-x) = -f(x), symmetric about the origin

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7
Q

Compound interest formula

A

P(1 + r/n)^nt, principal P, annual interest rate r compounds n times per year t

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8
Q

Continuously Compounded Interest

A

Pe^rt, an account begins with principal P and earns annual interest r compounded continuously

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9
Q

Half-life

A

A(t) = P(1/2)^t/h, the amount of material present at time t, where h is the half-life

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10
Q

e

A

As n approaches infinity, (1 + 1/x)^x

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11
Q

Identity Function

A

f(g(x)) = g(f(x))

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12
Q

a^log_a(x) where x,a>0, a doesn’t equal 1

A

x

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13
Q

log_a(a^x), a>0 for all x

A

x

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14
Q

log_a(xy)

A

log_a(x) + log_a(y)

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15
Q

log_a(x/y)

A

log_a(x) - log_a(y)

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16
Q

log_a(x)^y

A

ylog_a(x)

17
Q

For a function to have an inverse

A

Each output is associated with an input

18
Q

Domain if log_a(x)

A

Range of a^x, (0, infinity)

19
Q

Range of log_a(x)

A

Domain of a^x, (-infinity, infinity)

20
Q

Domain, range, period of y = tanx

A

D: x doesn’t equal kpi/2, k is an odd integer
R: (-infinity, infinity)
P: pi

21
Q

Domain, range, and period of y = secx

A

D: x doesn’t equal kpi/2, k is an odd integer
R: (-infinity, -1]U[1, infinity)
Period: 2pi

22
Q

Domain, range, and period of y = cscx

A

D: x doesn’t equal npi, n is an integer
R: (-infinity, -1]U[1, infinity)
P: 2pi

23
Q

Domain, range, and period of y = cotx

A

D: x doesn’t equal npi, n is any integer
R: (-infinity, infinity)
P: pi

24
Q

Domain and range of cos^-1(x)

A

D: [-1, 1]
R: [0, pi]

25
Q

Domain and range of y = sin^-1(x)

A

D: [-1, 1]
R: [-pi/2, pi/2]

26
Q

Domain and range of tan^-1(x)

A

D: (-infinity, infinity)
R: (-pi/2, pi/2)

27
Q

Domain and range of sec^-1(x)

A

D: (-infinity, -1]U[1, infinity)
R: [0, pi], y doesn’t equal pi/2

28
Q

Domain and range of csc^-1(x)

A

D: (-infinity, -1]U[1, infinity)
R: [-pi/2, pi/2], y doesn’t equal 0

29
Q

Domain and range of y = cot^-1(x)

A

D: (-infinity, infinity)
R: (0, pi)