Study

Question 1

What do real number include?

Answer 1

Include Irrational, rational, and integer numbers.

Question 2

Include Irrational, rational, and integer numbers.

Answer 2

Real numbers

Question 3

What does the € symbol mean?

Answer 3

“In”

Question 4

Symbol that means “in”

Answer 4

€

Question 5

The four ways to represent a function?

Answer 5

Graphically, algebraically, numerically using tables, verbally.

Question 6

Graphically, algebraically, numerically using tables, verbally.

Answer 6

The four ways to represent a function

Question 7

What makes graph not a function?

Answer 7

Does not pass vertical line test and has has two values of y for every x.

Question 8

Does not pass vertical line test and has has two values of y for every x.

Answer 8

Not a function.

Question 9

Draw graph of hot water faucet.

Answer 9

S

Question 10

How is this factored?:

2x^2-5x-12

Answer 10

Multiply the first and last constants and see what adds to the second number and multiplies to the last.

Question 11

Multiply the first and last constants and see what adds to the second number and multiplies to the last.

Answer 11

Dealing with unfactorable functions.

Question 12

How do you test if two functions (f(x) and g(x)) are inverses of each other?

Answer 12

Plug g(x) into f(x) and f(x) into g(x) and if you get x on both functions, they are inverses.

Question 13

How is the function f(x)=|x| written in piecewise form?

Answer 13

{ -x if x< 0

{ x if x>= 0

Question 14

{ -x if x< 0

{ x if x>= 0

Answer 14

Piecewise version of the function f(x)=|x|

Question 15

How can you test if a function is even?

Answer 15

If its graph is symmetric across the y-axis and f(x)=f(-x)

Question 16

If its graph is symmetric across the y-axis and f(x)=f(-x)

Answer 16

Testing if a function is even.

Question 17

Increasing function definition.

Answer 17

x1 < x2 and f(x1) < f(x2)

Question 18

x1 < x2 and f(x1) < f(x2)

Answer 18

Increasing function definition

Question 19

In an even function on the graph, is the function increasing or decreasing?

Answer 19

Neither (points upward both sides)

Question 20

When is a function neither increasing nor decreasing on a graph?

Answer 20

When it is even (points upward both sides)

Question 21

3 examples of real world mathematical models of functions.

Answer 21

Population size, demand of a product, falling object

Question 22

Population size, demand of a product, falling object

Answer 22

Examples of real world mathematical models of functions.

Question 23

Slope intercept form

Answer 23

y=mx+b

Question 24

y=mx+b

Answer 24

Slope intercept form

Question 25

Point Point form

Answer 25

m=y2-y1/x2-x1

Question 26

m=y2-y1/x2-x1

Answer 26

Point Point form

Question 27

How is a polynomial function defined?

Answer 27

P(x)=a(n)x^n + a(n-1)x^n-1 + ... a(1)x(1) + a(0)

Question 28

P(x)=a(n)x^n + a(n-1)x^n-1 + ... a(1)x(1) + a(0)

Answer 28

Polynomial function definition

Question 29

What is the domain of a polynomial?

Answer 29

All reals

Question 30

Have domain of all reals

Answer 30

Polynomials

Question 31

How many roots does the graph of a function NOT touching the x-axis have?

Answer 31

None

Question 32

What kind of graph of a function has no roots?

Answer 32

A function not touching the x-axis

Question 33

How can you tell how many roots a function has with this?: b^2 -4ac

Answer 33

< 0, no real roots > 0, 2 real roots = 0, 1 real root

Question 34

< 0, no real roots > 0, 2 real roots = 0, 1 real root

Answer 34

Using b^2 -4ac to find roots

Question 35

Power function

Answer 35

f(x)=x^a where “a” is a real number

Question 36

f(x)=x^a where “a” is a real number

Answer 36

Power function

Question 37

What makes a function not a polynomial?

Answer 37

Power is not an integer

Question 38

When the power of a function is not an integer, it is not a

Answer 38

Polynomial

Question 39

How do you graph ^3√x or any other odd denominator power?

Answer 39

Similar to x^3 but the graph gets flatter along the y-axis

Question 40

Similar to x^3 but the graph gets flatter along the y-axis

Answer 40

Graphs with odd roots as powers

Question 41

Graph f(x)=x^-1 OR 1/x

Answer 41

A

Question 42

What is a hyperbola?

Answer 42

Function with x and y-axis’ as its asymtotes

Question 43

Function with x and y-axis’ as its asymtotes

Answer 43

Hyperbola

Question 44

How is a rational number defined?

Answer 44

P/q, where both P and q are integers

Question 45

P/q, where both P and q are integers

Answer 45

Rational number

Question 46

What does the “pipe” “|” mean in a domain?

Answer 46

“Such that”

Question 47

Means “such that”

Answer 47

“Pipe” “|” in domains

Question 48

How makes a rational function?

Answer 48

Square roots or division

Question 49

Square roots and division make what kind of function?

Answer 49

Rational

Question 50

How is a sin graph plotted?

Answer 50

With 0 at 0 and period every π

Question 51

With 0 at 0 and period every π

Answer 51

Sin graph

Question 52

How is the cos graph plotted?

Answer 52

0 at 1 and period every π/2

Question 53

0 at 1 and period every π/2

Answer 53

Cos graph

Question 54

What is odd and what is even?: sin and cos

Answer 54

Sin is odd, cos is even

Question 55

What is the domain of sinx/cosx and why?

Answer 55

{x€R|x≠π/2 + nπ} because every π/2, sin is 0. Adding π to π/2 gives another multiple of π/2.

Question 56

What are three features of polynomial graphs?

Answer 56

No breaks, holes, or corners

Question 57

No breaks, holes, or corners

Answer 57

Polynomial graphs

Question 58

What is a characteristic of log graphs?

Answer 58

They always have (1,0) as a point

Question 59

They always have (1,0) as a point

Answer 59

Log graphs

Question 60

Exponential function definition

Answer 60

b^x ehere b>0

Question 61

b^x ehere b>0

Answer 61

Exponential function

Question 62

Characteristic of exponential function graphs

Answer 62

Always hit the point (0,1)

Question 63

Always hit the point (0,1)

Answer 63

Exponential functions

Question 64

What happens to a log graph as the base gets bigger?

Answer 64

It gets lower and closer to y-axis

Question 65

Gets lower and closer to y-axis as base b gets bigger

Answer 65

Log graphs

Question 66

What is vertex form?

Answer 66

y=a(x-h)^2 +k where (h,k) is the vertex