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Calculus Quiz Days 1-4 > Study > Flashcards

Study Flashcards

1
Q

What do real number include?

A

Include Irrational, rational, and integer numbers.

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2
Q

Include Irrational, rational, and integer numbers.

A

Real numbers

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3
Q

What does the € symbol mean?

A

“In”

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4
Q

Symbol that means “in”

A

€

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5
Q

The four ways to represent a function?

A

Graphically, algebraically, numerically using tables, verbally.

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6
Q

Graphically, algebraically, numerically using tables, verbally.

A

The four ways to represent a function

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7
Q

What makes graph not a function?

A

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

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8
Q

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

A

Not a function.

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9
Q

Draw graph of hot water faucet.

A

S

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10
Q

How is this factored?:

2x^2-5x-12

A

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

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11
Q

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

A

Dealing with unfactorable functions.

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12
Q

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

A

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

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13
Q

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

A

{ -x if x< 0

{ x if x>= 0

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14
Q

{ -x if x< 0

{ x if x>= 0

A

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

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15
Q

How can you test if a function is even?

A

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

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16
Q

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

A

Testing if a function is even.

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17
Q

Increasing function definition.

A

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

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18
Q

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

A

Increasing function definition

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19
Q

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

A

Neither (points upward both sides)

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20
Q

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

A

When it is even (points upward both sides)

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21
Q

3 examples of real world mathematical models of functions.

A

Population size, demand of a product, falling object

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22
Q

Population size, demand of a product, falling object

A

Examples of real world mathematical models of functions.

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23
Q

Slope intercept form

A

y=mx+b

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24
Q

y=mx+b

A

Slope intercept form

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25
Q

Point Point form

A

m=y2-y1/x2-x1

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26
Q

m=y2-y1/x2-x1

A

Point Point form

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27
Q

How is a polynomial function defined?

A

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

28
Q

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

A

Polynomial function definition

29
Q

What is the domain of a polynomial?

A

All reals

30
Q

Have domain of all reals

A

Polynomials

31
Q

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

A

None

32
Q

What kind of graph of a function has no roots?

A

A function not touching the x-axis

33
Q

How can you tell how many roots a function has with this?:

b^2 -4ac

A

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

34
Q

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

A

Using b^2 -4ac to find roots

35
Q

Power function

A

f(x)=x^a where “a” is a real number

36
Q

f(x)=x^a where “a” is a real number

A

Power function

37
Q

What makes a function not a polynomial?

A

Power is not an integer

38
Q

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

A

Polynomial

39
Q

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

A

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

40
Q

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

A

Graphs with odd roots as powers

41
Q

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

A

A

42
Q

What is a hyperbola?

A

Function with x and y-axis’ as its asymtotes

43
Q

Function with x and y-axis’ as its asymtotes

A

Hyperbola

44
Q

How is a rational number defined?

A

P/q, where both P and q are integers

45
Q

P/q, where both P and q are integers

A

Rational number

46
Q

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

A

“Such that”

47
Q

Means “such that”

A

“Pipe” “|” in domains

48
Q

How makes a rational function?

A

Square roots or division

49
Q

Square roots and division make what kind of function?

A

Rational

50
Q

How is a sin graph plotted?

A

With 0 at 0 and period every π

51
Q

With 0 at 0 and period every π

A

Sin graph

52
Q

How is the cos graph plotted?

A

0 at 1 and period every π/2

53
Q

0 at 1 and period every π/2

A

Cos graph

54
Q

What is odd and what is even?:

sin and cos

A

Sin is odd, cos is even

55
Q

What is the domain of sinx/cosx and why?

A

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

56
Q

What are three features of polynomial graphs?

A

No breaks, holes, or corners

57
Q

No breaks, holes, or corners

A

Polynomial graphs

58
Q

What is a characteristic of log graphs?

A

They always have (1,0) as a point

59
Q

They always have (1,0) as a point

A

Log graphs

60
Q

Exponential function definition

A

b^x ehere b>0

61
Q

b^x ehere b>0

A

Exponential function

62
Q

Characteristic of exponential function graphs

A

Always hit the point (0,1)

63
Q

Always hit the point (0,1)

A

Exponential functions

64
Q

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

A

It gets lower and closer to y-axis

65
Q

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

A

Log graphs

66
Q

What is vertex form?

A

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

Calculus Quiz Days 1-4 (1 decks)

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