1. Section 1.1 – Interval Notation

2. Objectives
*Review previously learned formulas. *Write things in interval notation.

3. Plotting points
Plot the following points on the coordinate plane: (4,-3) (7,1) (-1,5) (-3,-6) Which quadrant do each of them lie in?

4. Quadrants

5. Finding the distance between two points
There are three different ways that we can do this:

6. Method #1
This method only works when the two points share the same x-coordinate or y- coordinate. Example: Find the distance between (2,6) and (14,6)

7. Examples Find the distance: (-4,3) & (8,3) (2,-1) & (18,-1)
(4,0) & (10,0)

8. Method #2
Plot the following points on the coordinate plane and find the distance: (-2,5) & (6,4)

9. Pythagorean Theorem
The sum of the squares of the legs of a right triangle equals the square of the hypotenuse, so:

10. Finding the distance between two points using Pythagorean Theorem
Plot the following points on the coordinate plane and find the distance: (4,2) & (-1,3)

11. Method #3 – Distance Formula
We can use the distance formula to find the distance between any two points.

12. Example Using Distance Formula
Find the distance between the points (-4,8) and (6,5).

13. Now you try…
Find the distance between the two points using any method.
(5,2) & (14,2)
(-3,7) & (0,4)
(6,8) & (-1,3)
(5,5) & (2,1)

14. Interval Notation
Interval Notation is a method for writing down a set of numbers.
There are three different types of interval notation:
Open Intervals
Half-Open Intervals
Closed Intervals

15. Open Intervals
Write the following in interval notation: “All values of x such that x is greater than 7.” “All values of x such that x is less than -2” *We use _____________ when we are not including the number!

16. Half-Open Interval
Write the following in interval notation: “All values of x such that x is greater than or equal to 5 and less than 21.” “All values of x such that x is less than or equal to 16 and greater than 2.” *We use ___________ when the number is included.

17. Closed Interval
Write the following in interval notation: “All values of x that are greater than or equal to 4 and less than or equal to 6.” “All values of x that are greater than or equal to 8 and less than or equal to 14.”

18. More Examples… x is greater than 4 or x is less than -5.
x is greater than or equal to 8 or x is less than 2.
x<5 or x>10
x≤14 or x≥19

19. Worksheet