ALGEBRA + FUNCTIONS

ALGEBRA

Domain of a linear function (y=mx+b)

ARN

Domain of a quadratic function (exponent 2)

ARN

Domain of a polynomial function (exponent 3+)

ARN

“open dot"

not included, parenthesis

“closed dot"

included, brackets

are infinity brackets or parenthesis? why?

parenthesis, you can never reach infinity

If a function has no fractions or root the domain is

ARN

What is a reciprocal function?

a function where the x is a denominator in a fraction. (think 1 over)

What can the domain of a reciprocal never equal?

0, , any number/0 is undefined

What is the rule for exclusionary functions such as reciprocals?

you will always have one more pair than you exclude (ex: if function cannot include two numbers your domain will include three parts)

How do we join a set of ordered pairs when describing the domain and range?

with a union “U“ between each set

what does a union mean in algebra?

“or“

what is true for all CUBE and ODD square root functions

they can be negative or positive + the domain is ARN

what is true for all SQUARE and EVEN square root functions

they CANNOT be negative

What MUST you do to SQUARE and EVEN root functions when they’re on the top?

set the function as “> or equal to” 0

What MUST you do to SQUARE and EVEN root functions when they’re on the bottom?

set the function as “>” 0 (find x’s and exclude)

How do you find domain?

look from left to right (x’s)

How do you find range?

look from bottom to top (y’s)

unbounded functions have

and infinity on either side

bounded functions have

set points only (open and closed dots no arrows)

what is this called: f(x+h)-f(x)/h

a difference quotient

what can a difference quotient help you find?

the distance between a couple of points on a curve

(x+h)(x+h)

x²+2hx+h²

linear graph

straight line (y=mx+b)

quadratic graph

parabola’s/U graphs (exponent of 2)

How to find range of a quadratic

your lowest y will be your “b“ term (ex: y=x2+3 or y=x2-3, R: (-3,infinity), (3,infinity))

what does a negative sign in front of the first x do to the range of a parabola?

flip the function, y goes to negative infinity instead (ex:4-x², R: (4, negative infinity)

How to find the range on a parabola?

1) does the graph open up or down (- in front of x²)?

2) Find the x of the Vertex (lowest point on the graph, (x,y))

a) x=-b/2a, where b=second value + c= third

b) plug in x to find y + the ordered pair=vertex

3) the “y” of your vertex is your lowest y value

range of a cubic/odd polynomial

ARN

absolute value function graph

“V” graph

|x-2| or (x-2)

shifts to the right

|x+2| or (x+2)

shifts to the left

even radical graph (square + even roots)

point+curve graph (√x, +,+, opens to +,+ quadrant, R:(0, negative infinity))

x+2x+4

shift to the right four (opposite (-4) would shift to left)

a negative/positive sign inside a radical

impacts x (curve points to the left or right)

a negative/positive sign outside a radical

impacts y (curve points to the up or down)

if you don’t know or want to check what direction a radical function is going

plug in for x and see!!!

Composition

ex: (f o g(x)) combining the entire function

Combination

any of the basic methods (+,-,x,/), (f+g)(x), etc.