**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

C= What you start with

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:**

1. Read the problem

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

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