Chapter 1 Concept Map

Chapter 1 Concept Map

1. Independent Variable

   • X-axis
     • Domain: All X-values smallest to largest
       • Use parenthesis if you have infinity or open circle
         • Use square brackets for whole numbers
     • Input
       • Example: x=number of tickets sold

2. Dependent Variable

   • Y-axis
     • Range: All Y-values smallest to largest
     • Output
       • Example: y= number of other tickets

3. Graph Definitions

   • Relation-any set of ordered pairs
   • Ordered Pair- coordinates on a graph
     • Example: (3,4) x=3, y=4
   • Function- Every input has only ONE output
     • Function Notation: y=f(x)
       • Example equation: y=x+2 Function equation f(x)= x+2
   • Vertical Line Test: use to test if the equation is a function.

4. TYPES OF GRAPHS

   • Constant: y=0x+ number
   • Linear: y=mx+b
     • Example: y=3x+4
   • Absolute Value: y= |x|
   • Quadratic: y=x squared
   • Cubic: y= x cubed
   • Square Root: y= the square root of x
   • Cube root: x= the cubic root of x

5. INEQUALITIES

   • if you multiply/divide by a negative number, remember to flip the symbol
   • Example: 3x+5<x-17
     • Subtract x to both sides
       • 2x+5<-17
         • subtract 5 to both sides
           • 2x<-22
             • Divide by 2
               • x<-11

6. Solving Basic Equations

   • Example: b squared+144=0
     • b squared = the square root of negative 144
       • b= no solution
         • You can't square root a negative number

7. Making and Using Formulas

   • Example: The number of H of hours in d days
     • H= 24d
       • Another Example: The area of a rectangle whose length is three times its width w
         • A=3w