PreCalc Chapter 1 Test Flashcards Preview

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Flashcards in PreCalc Chapter 1 Test Deck (75)
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0
Q

How can you tell if a function is even? What kind of symmetry does it have?

A

Plug in -x for x, and your equation will remain exactly the same {{f(x)}}
Reflection symmetry over the y-axis

1
Q

how do you know if a function is odd? What kind of symmetry does it have?

A

Plug in -x for x and your equation will be -f(x) (exact opposite). It has rotational symmetry 180 degrees about the origin

2
Q

if your function is not odd or even, what is it? what kind of symmetry does this kind of function have

A

neither–no symmetry

3
Q

what are points of inflection

A

where concavity changes

4
Q

which way do you view a graph to tell if it is increasing or decreasing

A

left to right

5
Q

what is the difference between intercepts, roots, and zeroes?

A

no difference

6
Q

what does an open point signify on a graph

A

that breaks one of the rules in your piecewise function rules

7
Q

how would you express that your domain can be all real numbers greater than -2 using interval notation

A

Domain= {R’s: (-2, [infinity sign])}

8
Q

what is a secant line

A

a line that intersects two points

9
Q

A ________________ is a location on a graph where your line stops increasing and starts decreasing

A

relative max

10
Q

The ________ ________ ________ is used to determine whether the graph of an equation is a function of y in terms of x

A

Vertical Line Test

11
Q

The _______ of a function f are the values of x for which f(x)=0

A

zeroes (roots, x-intercepts)

12
Q

A function f is ______ on an interval when, for any x1 and x2 in the interval, x1 is less than x2 implies f(x1) is greater than f(x2)

A

decreasing

13
Q

The ______ ______ _______ _______ between any two points (x1, f(x1)) and (x2, f(x2)) is the slope of the line through the two points, and this lines is called the _____ line

A

average rate of change, secant

14
Q

A function f is _____ when, for each x in the domain of f, f(-x)=-f(x)

A

odd

15
Q

true or false- a function with a square root cannot have a domain that is the set of all real numbers

A

false– the x value could be raised to an even root underneath the square root
i.e. y=square root of x^2

16
Q

if the graph of a function was a) even or b) odd. what ordered pair could also lie on that graph if (-5/3, -7) did

A

a) (5/3, -7)

b) (5/3, 7)

17
Q

what is domain

A

set of all values that the independent variable (usually x) can be

18
Q

what is the range

A

the set of all values that the dependent variable (usually y) can be

19
Q

what does relation mean

A

set of ordered pairs (mapping, x/y chart, etc.)

20
Q

what is f(1)=4 in simpler terms?

A

(1,4) an ordered pair

21
Q

what is a function

A

a specific relation saying your x value can never produce two or more y values

22
Q

true or false– if an equation has a y value which produces 2 x values, it is NOT a function

A

false- although an x value cannot produce two or more y values, a y value can produce two or more x values

23
Q

what is a piecewise function

A

a function with multiple equations, each with designated rules

24
Q

what is (x^2-1) said to be

A

difference of perfect squares

25
Q

what is implied domain

A

values acceptable for x for a certain function (given)

usually in in piecewise

26
Q

what is the variable under the radical called

A

radicand

27
Q

how do you solve a difference quotient

A

make two large brackets, plug in when they are asking you to. simplify and solve

28
Q

how do you express that the domain of a function is x greater than or equal to 1 in interval notation. What notation is it in above?

A

[-1, infinity) inequality

29
Q

A relation that assigns to each element x from a set of inputs, or _________, exactly one element y in a set of outputs, or ______, is called a ______.

A

domain, range, function

30
Q

For an equation that represents y as a function of x, the set of all values taken on by the ________ variable x is the domain, and the set of all values taken on by the ______ variable is the range

A

independent, dependent

31
Q

If the domain of the function f is not given, then the set of values of the independent variable for which the expression is defined is called the ___________.

A

implied domain

32
Q

In calculus, one of the basic definitions is that of a ___________, given f(x+h)-f(x)/h, h cannot =0

A

difference quotient

33
Q

What is standard form

A

Ax+By=C

34
Q

What is point slope form

A

y2-y1=m(x2-x1)

35
Q

what is slope intercept form

A

y=mx+b

36
Q

what is slope formula

A

y2-y1/x2-x1

37
Q

how would you find the equation of a line parallel to y=3x-7 through (4,1)

A

your slope is 3, then plug in 4 for x, 1 for y, and 3 for m (in slope intercept) and solve for b.
OR–plug (4,1) in point slope form with m as 3

38
Q

the simplest mathematical model for relating two variables is the ____ equation in two variables y=mx+b

A

linear

39
Q

For a line, the ratio of the change in y to the change in x is called the __ of the line

A

slope

40
Q

The _____________ form of the equation of a line with slope m passing through (x1, y1) is y1-y2=m(x2-x1)

A

point slope

41
Q

Two lines are ______ iff their slopes are equal

A

parallel

42
Q

Two lines are ______ iff their slopes are negative reciprocals of each other

A

perpendicular

43
Q

When the x-axis and the y-axis have different units of measure, the slope can be interpreted as a ______

A

rate

44
Q

The prediction method __________ is the method used to estimate a point on a line when the point does not lie between the given points

A

linear extrapolation

45
Q

Every line has an equation that can be written in __ form

A

standard

46
Q

Polynomial functions are _________ and ___________

A

continuous and curvy

47
Q

what is the parent function for absolute value?

A

y=IxI

48
Q

how do you know if an equation’s graph has x-axis symm? y-axis? origin?

A

x- plug in negative for y, must be the same
y- plug in negative for x, must be the same
origin- plug in - for both, must be the same

49
Q

an odd exponent (x^3) signifies what

A

that the graph will got through each intercept (no repeats)

50
Q

what is the equation of a circle

A

(x-h)^2+(y-k)^2=r^2
center (h,k)
radius r

51
Q

what does { mean?

: ?

A

set, such that

52
Q

An ordered pair (a,b) is a ______ of an equation in x and y when the substitutions x=a and y=b result in a true statement

A

solution

53
Q

The set of all solution points of an equation is the ___ of the equation

A

graph

54
Q

The points at which a graph intersects or touches an axis are called the ______ of the graph

A

intercepts

55
Q

A graph is symmetric with respect to the _____if, whenever (x,y) is on the graph, (-x,y) is also on the graph

A

y-axis

56
Q

when you construct and use a table to solve a problem, you are using a ______ approach

A

graphic

57
Q

what is another name for the coordinate system, where does it come from

A

cartesian plane, Rene Descarte

58
Q

distance formula is derived from ______

A

pythagorean theorem

59
Q

what are the types of transitions

A

dilation, reflection, rotation

60
Q

translation means ____

A

slide

61
Q

what is percentage increase (or decrease)

A

amount increase/original amount

62
Q

An ordered pair of real numbers can be represented in a plane called the rectangular coordinate system or the ____ plane

A

cartesian

63
Q

The point of intersection of the x axis and the y axis is the ________, and the two axes divide the coordinate plane into four parts called ____

A

origin, quadrants

64
Q

the ___________ is a result derived from the pythagorean theorem

A

distance formula

65
Q

Finding the average values of the representative coordinates of the two endpoints of a line segment in a coordinate plane is also known as using the

A

midpoint formula

66
Q

what axis does your independent variable (x) go on? (y)?

A

x, y

67
Q

what would the graph x=2 look like?

y=3?

A

vertical line through 2

horizontal through 3

68
Q

intercepts are written in

A

ordered pairs

69
Q

what is intercept form

A

x/a + y/b = 1

when a does not equal nor b does not equal 0

70
Q

how do you determine if an equation represents y as a function of x

A

set it equal to y–determine if one x value could produce two y values

71
Q

when writing an equation as a function of another equation, look for

A

shared variables

72
Q

when a graph is constant, you always express the ordered pair with _______

A

brackets [ ]

73
Q

how do you find average rate of change

A

F(new x) - F(old x)/new x-old x

74
Q

height=

length=

A

top-bottom

right-left