Interval and Set Builder Notation:
- Example: Describe all multiples of seven using set builder notation: {X|X=7n, n E Z}
- "X|" means X such that.
- Then you have your "X=" which literally means x equals.
- The "7" is the actual number you start with and the "n" is any multiple of 7.
- "E" stands for the element of.
- "Z" is any of your real numbers.
- Example: Write X>-4 using interval notation: (-4, ∞).
- ( )- means that the numbers aren't included
- [ ]- means that the numbers are included
- < > - means the the numbers aren't included
- ≤ ≥ - means the the numbers are included
- Example: -2 ≤ C ≤ 12 use set interval notation: [-2,12]
- When there are two inequalities they are in union with one another
- Example: write X<3 or X> 54 using interval notation: (-∞, 3) U (54, ∞)
- Set Builder Notation:
- Example: Describe all multiples of seven using set builder notation: {X|X=7n, n E Z}
- "X|" means X such that.
- Then you have your "X=" which literally means x equals.
- The "7" is the actual number you start with and the "n" is any multiple of 7.
- "E" stands for the element of.
- "Z" is any of your real numbers.
- Interval Notation:
- Example: Write X>-4 using interval notation: (-4, ∞).
- ( )- means that the numbers aren't included
- [ ]- means that the numbers are included
- < > - means the the numbers aren't included
- ≤ ≥ - means the the numbers are included
- Example: -2 ≤ C ≤ 12 use set interval notation: [-2,12]
- When there are two inequalities they are in union with one another
- Example: write X<3 or X> 54 using interval notation: (-∞, 3) U (54, ∞)
- Vertical Line Test:
-
- If an equation says that the x's don't repeat then it passes the test, also if the x's do repeat the y's have to too. But if the x repeats then it doesn't pass.
- Chart Example: X:1,3,4,4,5,7
Y: 4,5,8,12,23
-This chart would fail the vertical line test because the Y's don;t repeat when the X's do.
- Finding the Domain:
- Example: 4X-1 > 0
- Example: Function defined when 2X-3=0
Domain= {x|x>3/2, x E R}
- Piecewise Functions:
- Your x value plugs into which ever inequality it fits in
- solve the equation that corresponds with the inequality
- Example: Find the average price per square foot for a home with the square footage of 1400 square feet:
Inequality: a-1000/40 +75 1400-1000=400 400/40=10 10+75=85