Unit 1: Functions
A Function is a relationship that has an output for every one point.
Vertical Line Test:
X’s (input) cannot repeat. Make sure the X or the input doesn’t appear more than once.
The symbol f(x) replaces Y in the equation.
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:
C= What you start with
1+r= growth rate
1-r= the decay rate
Exponential Graphs can never go below the x-axis. They will always stay in the positive.
Linear Graphs: Graphs that make a straight line.
Quadratic Graphs: Graphs that make a parabola (U-Shape)
Exponential Growth and Decay Graphs: Make half a U-Shape and never goes below the x-axis
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
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