Section 1.1 – Interval Notation

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Presentation transcript:

Section 1.1 – Interval Notation

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

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?

Quadrants

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

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)

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

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

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

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)

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

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

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)

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

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!

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.

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.”

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

Worksheet