Pre-Requisites

Question 1

Slope is a ___ ___ between x and y increments.

Answer 1

constant ratio

Question 2

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

Answer 2

independent variable, dependent variable

Question 3

Increment

Answer 3

Change in a variable

Question 4

Implied domain

Answer 4

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.

Question 5

Even function

Answer 5

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

Question 6

Odd function

Answer 6

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

Question 7

Compound interest formula

Answer 7

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

Question 8

Continuously Compounded Interest

Answer 8

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

Question 9

Half-life

Answer 9

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

Question 10

e

Answer 10

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

Question 11

Identity Function

Answer 11

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

Question 12

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

Answer 12

x

Question 13

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

Answer 13

x

Question 14

log_a(xy)

Answer 14

log_a(x) + log_a(y)

Question 15

log_a(x/y)

Answer 15

log_a(x) - log_a(y)

Question 16

log_a(x)^y

Answer 16

ylog_a(x)

Question 17

For a function to have an inverse

Answer 17

Each output is associated with an input

Question 18

Domain if log_a(x)

Answer 18

Range of a^x, (0, infinity)

Question 19

Range of log_a(x)

Answer 19

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

Question 20

Domain, range, period of y = tanx

Answer 20

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

Question 21

Domain, range, and period of y = secx

Answer 21

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

Question 22

Domain, range, and period of y = cscx

Answer 22

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

Question 23

Domain, range, and period of y = cotx

Answer 23

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

Question 24

Domain and range of cos^-1(x)

Answer 24

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

Question 25

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

Answer 25

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

Question 26

Domain and range of tan^-1(x)

Answer 26

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

Question 27

Domain and range of sec^-1(x)

Answer 27

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

Question 28

Domain and range of csc^-1(x)

Answer 28

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

Question 29

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

Answer 29

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