## Algebra: Unit 1 Functions

Unit 1: Functions

A Function is a relationship that has an output for every one point. Vertical Line Test:

No matter where you draw a vertical line, it will only cross the graphed line once. X’s (input) cannot repeat. Make sure the X or the input doesn’t appear more than once. This is a function because the X (input) doesn’t appear more than once.

Function Notation:

The symbol f(x) replaces Y in the equation.

ex: f(x)=2x=1

y=2x=1

The Independent Variable is the input variable of a function (x). It is not affected by anything else, and it doesn’t depend on anything. The Dependent Variable is the output of a function (y). It is affected by others, and it’s dependent on other variables.

Domain and Range:

Exponential Growth and Decay:

Exponential Growth:

y=C(1+r)t

r= rate

t= time

1+r= growth rate

Exponential Decay:

y=C(1-r)t

1-r= the decay rate

Exponential Graphs: Exponential Graphs can never go below the x-axis. They will always stay in the positive.

Analyze Data

Linear Graphs: Graphs that make a straight line.

y=mx+b Quadratic Graphs: Graphs that make a parabola (U-Shape)

y=ax^2=bx+c Exponential Growth and Decay Graphs: Make half a U-Shape and never goes below the x-axis

y=a^x Variation Equations

Direct Variation: A situation in which two quantities increase or decrease at the same rate. (constant) Always linear that goes through (0,0) Inverse Variation: A situation in which one quantity increases while another decreases. It never hits zero. Writing Algebraic Expressions/Equations:

2. Find the unknown and label it with an X

3. Find the key math words and circle them

4. Replace the words with the math symbols and write the expression

Vocabulary

Variables: A letter used to represent an unknown value

Numerical Expression: A grouping of numbers and operations

ex: 2+3       7-4       6×5      72/9

Variable Expression: A group being of numbers with a variable

ex: 2+x        x-8      10n     g/7