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Pre-Calc > Test 1 (2.2-3.5) > Flashcards

Test 1 (2.2-3.5) Flashcards

1
Q

Slope

A

m=(y2-y1)/(x2-x1)

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2
Q

Average rate of exchange

A

Δy/Δx

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3
Q

vertical line

A

x=a

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4
Q

point slope form of a line

A

y-y1=m(x-x1)

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5
Q

horizontal line

A

y=b

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6
Q

slope-intercept form

A

y=mx+b

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7
Q

general form of a line

A

Ax+By=C

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8
Q

Standard form of an equation of a circle

A

(x-h)(squared)+(y-k)(squared)=r(squared)

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9
Q

general form of a circle

A

x(squared)+y(squared)+ax+by+c=0

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10
Q

direct variation

A

y=kx

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11
Q

inverse variation

A

y=k/x

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12
Q

joint variation

A

y=k(at)/x

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13
Q

the number k is called the

A

constant of proportionality

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14
Q

when the value of one variable is related to the value of a second variable it is called a

A

relation

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15
Q

a relation is

A

a correspondence between two sets

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16
Q

when speaking of functions we say x ___ to y or y ___ on x

A

corresponds, relies

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17
Q

how do you write x corresponds to y?

A

x—>y

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18
Q

x is the ___ and y is the ___

A

input, output

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19
Q

the set of all inputs for a relation is called

A

the domain

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20
Q

the set of all outputs for a relation is called

A

the range

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21
Q

a ___ is a special type of relation

A

function

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22
Q

Definition of a function

A

a function form X into Y is a relation that associates with each element of X exactly one element of Y

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23
Q

the set X is called the

A

domain

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24
Q

the set Y is called the

A

range

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25
Q

the corresponding y to set x is called the

A

value or the image of x

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26
Q

for a function no input has…

A

more than one output

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27
Q

for a function, the variable x is called the

A

independent variable

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28
Q

for a function, the variable y is called the

A

dependent variable

29
Q

the independent variable is also called the

A

argument of the function

30
Q

the difference quotient of a function f(x)

A

f(x+h)-f(x)/h when h≠0

31
Q

function implicit form

A

x+y=a

32
Q

function explicit form

A

y=f(x)=x

33
Q

steps for finding the domain of a function defined by an equation

A
  1. start with the domain as a set of all real numbers
  2. if the equation has a denominator, exclude any numbers that give a zero denominator
  3. if the equation has a radical of even index, exclude any numbers that cause the expression inside the radical to be negative.
34
Q

the sum f+g function is defined by

A

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

35
Q

the difference f-g function is defined by

A

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

36
Q

the product f•g function is defined by

A

(f•g)(x)=f(x)•g(x)

37
Q

the quotient f/g function is defined by

A

(f/g)(x)=f(x)/g(x) when g(x)≠0

38
Q

if any vertical line intersects a graph at more than one point, the graph is

A

not the graph of a function

39
Q

what is the vertical line test

A

a set of points in the xy plane is the graph of a function only if every vertical line intersects the graph in at most one point

40
Q

a function is ___ if for every number x in its domain the number -x is also in the domain and

A

even, f(-x)=f(x)

41
Q

a function is __ if for every number in its domain the number -x is also in the domain and

A

odd, f(-x)=-f(x)

42
Q

a function is even only if its graph is symmetrical in respect to__

A

the y axis

43
Q

a function is odd only if its graph is symmetrical in respect to__

A

the origin

44
Q

when describing the behavior of a function in terms of its increasing, decreasing, or constant, do so in terms of its __ values

A

x

45
Q

the __ value is the local minimum or maximum value of a function

A

y

46
Q

the absolute minimum and maximum values are also called the

A

absolute extrema or extrema values

47
Q

if f is a continuous function whose domain is a closed interval [a,b] then f has an absolute maximum and minimum value of

A

[a,b]

48
Q

equation for average rate of exchange of a function

A

Δy/Δx=f(b)-f(a)/b-a when a≠0

49
Q

secant line slope equation

A

f(b)-f(a)/b-a=f(a+h)-f(a)/h

50
Q

the average rate of change from points a to b equals the slope of the secant line containing the two points

A

(a,f(a)) and (bf(b))

51
Q

properties of function f(x)=√x

A
  1. The domain and range re a set of nonnegative real numbers.
  2. the x and y intercept of the graph is 0
  3. the function is neither even nor odd
  4. the function is increasing on interval [0,∞]
  5. the function has an absolute minimum of 0 at x=0
52
Q

properties of f(x)=∛x(cube root function)

A
  1. the domain and the range are a set of all real numbers
  2. the x and y intercept are 0
  3. the function is odd
  4. the function is increasing on interval (-∞,∞)
  5. the function does not have any local minima or maxima
53
Q

properties of f(x)=lxl(absolute value)

A
  1. the domain is a set of all real numbers, the range is {fly≥0}
  2. the x and y intercepts are 0
  3. the function is even
  4. the function is decreasing on interval (-∞,0] and increasing on interval [0,∞)
  5. the function has an absolute minimum of 0 at x=0
54
Q

constant function equation and appearance

A

f(x)=b when b is a real number, the graph should look like a horizontal line

55
Q

domain and range of constant function

A

domain: set of all real numbers
range: set consisting of a single number b

56
Q

identity function equation and appearance

A

f(x)=x, graph should appear as a linear line

57
Q

domain and range of identity function, slope, y intercept

A

domain and range are a set of all real numbers
slope is 1 and y intercept is 0
this function is odd

58
Q

domain and range of square function, intercept

A

domain: set of all real numbers
range: nonnegative real numbers
intercept at 0,0

59
Q

square function equation and appearance

A

f(x)=x^2, graph should appear as a parabola

60
Q

cube function equation

A

f(x)=x^3

61
Q

domain and range of cube function and intercept

A

domain and range are a set of all real numbers
intercept is 0,0
this function is odd

62
Q

square root function equation

A

f(x)=√x

63
Q

square root function domain and range and intercept

A

domain and range are a set of nonnegative real numbers and the intercept is 0,0, the is function is neither odd not even

64
Q

reciprocal function equation

A

f(x)=1/x

65
Q

domain and range of reciprocal function and intercepts

A

domain and range are set of all nonzero real numbers, the graph has no intercepts and is an odd function

66
Q

what does int(x) stand for

A

largest integer less than or equal to x

67
Q

equation and properties of int(x)

A

f(x)=intx=greater integer less than or equal to x

the domain is a set of all real numbers, the range is a set of integers

68
Q

a function is continuous if

A

you can draw it without picking up your penciled there are no gaping holes

69
Q

int(x) is also called

A

a step function

Pre-Calc (1 decks)

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