Chapter One: A Library of Functions

Question 1

What is a function and what is it used to rep?

Answer 1

Takes each input and assigns 1 output, used to rep dependency.

Question 2

What are properties of inputs?

Answer 2

Domain, independent.

Question 3

What are properties of outputs?

Answer 3

Range, dependent.

Question 4

What does discrete mean?

Answer 4

Quantities that only take certain values.

Question 5

What does continuous mean?

Answer 5

Use any number.

Question 6

When is a function linear?

Answer 6

When its slope is the same at every point.

Question 7

What is the form of a linear function?

Answer 7

y=mx+b

Question 8

When is a function increasing?

Answer 8

If values of f(x) increases as x increases.

Question 9

When is a function decreasing?

Answer 9

If values of f(x) decreases as x increases.

Question 10

When is a function monotonic?

Answer 10

If it increases for all x or decreases for all x.

Question 11

What is a common functionality relationship?

Answer 11

Proportionality - direct (y=kx) or inverse(y=k/x)

Question 12

What is the formula for an exponential function?

Answer 12

P=Pinitial*a^t

Question 13

How can you tell if a function is exponential or not?

Answer 13

The ratio for P values are the same for equally spaced t values.

Question 14

What are characteristics of exponential functions?

Answer 14

Concave up and down..

Question 15

When does an exponential function demonstrate growth?

Answer 15

When a>1

Question 16

When does an exponential function demonstrate decay?

Answer 16

When 0<a></a>

Question 17

What is the formula for exponential growth/decay?

Answer 17

P=Pinitiale^(kt) vs. P=Pinitiale^(-kt)

Question 18

What happens if a function is multiplied by a constant, c?

Answer 18

The graph will stretch or shrink vertically. If c is negative, it will also reflect the function over the x-axis.

Question 19

What is a composite function?

Answer 19

A function of a function.

Question 20

When is f(x) and even/odd function?

Answer 20

Even if f(x) = f(-x)

Odd if -f(x) = f(-x)

Question 21

What is the formula for an inverse function?

Answer 21

f(y)^-1 = x

Question 22

When is a function invertible?

Answer 22

If it is one-to-one,

Question 23

What do the graphs of inverse functions look like?

Answer 23

Reflection over the line y=x

Question 24

What are the properties of log functions?

Answer 24

log(AB)
log(A/B)
log(A^p)
log(10^x)
10^(logx)

Question 25

Which two trig functions equal to one when added together?

Answer 25

cos^2x+sin^2x = 1

Question 26

Which trig fuction is even/odd?

Answer 26

``` sin = odd cos = even ```

Question 27

Define amplitude.

Answer 27

Helf the distance between min and max.

Question 28

Define period.

Answer 28

Smallest time needed for one complete cycle.

Question 29

What is the formula to convert from sin to cos?

Answer 29

sinx=cos(x-pi/2)