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

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

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

neither–no symmetry

what are points of inflection

where concavity changes

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

left to right

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

no difference

what does an open point signify on a graph

that breaks one of the rules in your piecewise function rules

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

Domain= {R’s: (-2, [infinity sign])}

what is a secant line

a line that intersects two points

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

relative max

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

Vertical Line Test

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

zeroes (roots, x-intercepts)

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

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

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

odd

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

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)

what is domain

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

what is the range

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

what does relation mean

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

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

(1,4) an ordered pair

what is a function

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

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

what is a piecewise function

a function with multiple equations, each with designated rules

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

difference of perfect squares

what is implied domain

values acceptable for x for a certain function (given)

usually in in piecewise

what is the variable under the radical called

radicand

how do you solve a difference quotient

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

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

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

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

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

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

difference quotient

What is standard form

Ax+By=C

What is point slope form

y2-y1=m(x2-x1)

what is slope intercept form

y=mx+b

what is slope formula

y2-y1/x2-x1

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

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

linear

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

slope

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

point slope

Two lines are ______ iff their slopes are equal

parallel

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

perpendicular

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

rate

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

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

standard

Polynomial functions are _________ and ___________

continuous and curvy

what is the parent function for absolute value?

y=IxI

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

an odd exponent (x^3) signifies what

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

what is the equation of a circle

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

center (h,k)

radius r

what does { mean?

: ?

set, such that

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

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

graph

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

intercepts

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

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

graphic

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

cartesian plane, Rene Descarte

distance formula is derived from ______

pythagorean theorem

what are the types of transitions

dilation, reflection, rotation

translation means ____

slide

what is percentage increase (or decrease)

amount increase/original amount

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

cartesian

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

the ___________ is a result derived from the pythagorean theorem

distance formula

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

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

x, y

what would the graph x=2 look like?

y=3?

vertical line through 2

horizontal through 3

intercepts are written in

ordered pairs

what is intercept form

x/a + y/b = 1

when a does not equal nor b does not equal 0

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

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

shared variables

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

brackets [ ]

how do you find average rate of change

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

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