Algebra 2-Unit 1

Intercepts

points where a line crosses the x-axis and y-axis

Ordered pairs

Intercepts are written as

Domain

The set of all possible x values where our graph exists

Interval or inequality

Domain notation

Range

The set of all possible y values where a graph exists

Interval or inequality

Range notation

Increasing interval

Between what x values is the slope positive (going up)

Decreasing interval

Between what x values is the slope negative (going down)

Increasing/ decreasing interval

What is this the notation for?
Increasing: (- infinity, -1]
Decreasing: [-1, 5]

Intercepts

What is this the notation for?
X: (5, 0)
Y: (0, 3)

Global/absolute max/min

The greatest possible and least possible y values on a function

Global/absolute max/min

What is this the notation for?
Abs max @ y=80
Abs min @ y= 5

Local/ relative min/max

The highest values and lowest values in a particular section of a graph. List ALL of the max and min values!

Local/ relative min/max

What is this the notation for?
Rel max @ y=45
Y=50
Y=25
Rel min @ y=10
Y=5
Y=1

End behavior

Describes how the function behaves at the ends of the graph

End behavior

What is this the notation for?
As x-> 0, y->7
As x->10, y->-3

Continuity

Describes weather a function has breaks, holes, or jumps. Is it one continuous line?

Relation

A relationship between sets of values

Function

A relation where every x value has exactly one y value. (No repeats of y values for any single x value)

F(x)=y

Function notation

G(x)=af(x-c)+d

The general equation used to represent any function transformation.

The transformed function

In the equation for function transformation, G(x) represents what?

Stretches, compresses and reflects functions

In the equation for function transformation, the variable a does what?

I a I>1

If the variable a is ______ then it will perform a vertical stretch on the function.

0

If the variable a is ______ then it will perform a vertical compression on the function.

a

If the variable a is ______ then it will perform a vertical reflection on the function.

Left

If the variable c is positive, (x+c) then the function moves to the _____.

Right

If the variable c is negative, (x-c) then the function moves to the _____.

Horizontal translations

The variable c in the general equation for translating equations does ______________ ______________.

Vertical translations

The variable d in the general equation for translating equations does __________ ______________.

up

If the variable d is positve (+d) then the function moves __.

Down

If the variable d is negative (-d) then the function moves ____.

1. Solve the equation for the inside function
2. Plug the solution for the inside function into the outside function
3. Solve for the outside function
4. The outside function is now the answer for this one.

What are the steps to perform in order to solve f(g(x))?
(There are equations for f(x) and g(x))

Inverse

This reverses the action of the original function and swaps the domain and range.

f^-1(x)

Notation for inverses=

A function

If the original function of the inverse passes the horizontal and vertical line tests then the inverse will also be ___.

x^2

An equation will be a parabola if it has a __ in it.

y=x

Inverses reflect over the line ___.

One-to-one functions

What is it called when both the original function and its inverse are functions?

System of equations

A set/collection of equations where the solution(s) to the system is the point where the 2 functions intersect

Coordinate point

The solution to a system of equations is always written as a ______.

Substitution

These are the steps for what way of solving a system of equations?
1.Isolate one of the variable in one of the equations
2. Plug the answer into the corresponding variable
3. Simplify and solve for the remaining variable
4. Plug in the answer from step 3 and solve for the value of the remaining variable
5. Put the answers in an ordered pair

Elimination

These are the steps for what way of solving a system of equations?
1. Multiply equation #1 by a number that will make it so that a variable in equation #2 is eliminated when they are added together.
2. Add the equations together and find the remaining variable's value
3.use substitution to find the other variable
4. Put answers into an ordered pair

peicewise function

A function built by 2+ equations. The first part is the y=mx+b of the figure, and the second part of one equation is the constraints.

Constraints

Each equation in a piecewise function has a specific domain assigned to it. Called ______.

Graphed

Every equation in a piecewise function can be _______.

Continuity

These are the steps for determining what?
1. Plug in the thing that x is relating to that are teh same in both equations into the x for all of the equations in the peicewise function
2. Solve for x
3. If x equals the same thing in every equation, then the it is _____.