Flashcards in PreCalc Chapter 1 Test Deck (75):

0

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

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

1

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

###
Plug in -x for x, and your equation will remain exactly the same {{f(x)}}

Reflection symmetry over the y-axis

2

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

### neither--no symmetry

3

## what are points of inflection

### where concavity changes

4

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

### left to right

5

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

### no difference

6

## what does an open point signify on a graph

### that breaks one of the rules in your piecewise function rules

7

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

### Domain= {R's: (-2, [infinity sign])}

8

## what is a secant line

### a line that intersects two points

9

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

### relative max

10

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

### Vertical Line Test

11

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

### zeroes (roots, x-intercepts)

12

## 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)

### decreasing

13

## 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

### average rate of change, secant

14

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

### odd

15

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

###
false-- the x value could be raised to an even root underneath the square root

i.e. y=square root of x^2

16

## 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) (5/3, -7)

b) (5/3, 7)

17

## what is domain

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

18

## what is the range

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

19

## what does relation mean

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

20

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

### (1,4) an ordered pair

21

## what is a function

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

22

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

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

23

## what is a piecewise function

### a function with multiple equations, each with designated rules

24

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

### difference of perfect squares

25

## what is implied domain

###
values acceptable for x for a certain function (given)

usually in in piecewise

26

## what is the variable under the radical called

### radicand

27

## how do you solve a difference quotient

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

28

## 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?

### [-1, infinity) inequality

29

## 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 ______.

### domain, range, function

30

## 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

### independent, dependent

31

## 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 ___________.

### implied domain

32

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

### difference quotient

33

## What is standard form

### Ax+By=C

34

## What is point slope form

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

35

## what is slope intercept form

### y=mx+b

36

## what is slope formula

### y2-y1/x2-x1

37

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

###
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

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

### linear

39

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

### slope

40

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

### point slope

41

## Two lines are ______ iff their slopes are equal

### parallel

42

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

### perpendicular

43

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

### rate

44

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

### linear extrapolation

45

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

### standard

46

## Polynomial functions are _________ and ___________

### continuous and curvy

47

##
what is the parent function for absolute value?

### y=IxI

48

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

###
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

## an odd exponent (x^3) signifies what

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

50

## what is the equation of a circle

###
(x-h)^2+(y-k)^2=r^2

center (h,k)

radius r

51

##
what does { mean?

: ?

### set, such that

52

## 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

### solution

53

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

### graph

54

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

### intercepts

55

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

### y-axis

56

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

### graphic

57

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

### cartesian plane, Rene Descarte

58

## distance formula is derived from ______

### pythagorean theorem

59

## what are the types of transitions

### dilation, reflection, rotation

60

## translation means ____

### slide

61

## what is percentage increase (or decrease)

### amount increase/original amount

62

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

### cartesian

63

## 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 ____

### origin, quadrants

64

## the ___________ is a result derived from the pythagorean theorem

### distance formula

65

## 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

### midpoint formula

66

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

### x, y

67

##
what would the graph x=2 look like?

y=3?

###
vertical line through 2

horizontal through 3

68

## intercepts are written in

### ordered pairs

69

## what is intercept form

###
x/a + y/b = 1

when a does not equal nor b does not equal 0

70

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

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

71

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

### shared variables

72

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

### brackets [ ]

73

## how do you find average rate of change

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

74