P.1

•Set Notation•Intersections of Sets

•Unions of Sets•Negative Properties and Algebraic Expressions

•Modeling Real Data with Algebraic Formulas

Pg. 14 # 20-34 even, 92, 96, 100, 120, 122, 124

Set notation is a tool that allows the writer to list a collection of letters or numbers (called elements) as members of the same group.

The Roster Method of representing sets denotes a complete list of a set’s elements separated by commas and contained within braces.

Here’s an example: {b, f, m, p, v, w}

This is the best method to use when sets are finite and small.

Note: Sometimes a writer must state that there are no elements in a set. This is called the empty set, which we represent with this symbol: Ø

Intersections of Sets:

“What is the intersection of these sets?” is the same question as “Which elements do these sets have in common?”

Question: {1, 2, 3} ∩ {2, 4, 6}

Answer: {2}

Question: {a, b, e, f} ∩ {b, f, g}

Answer: {b, f}

Sometimes the sets have no elements in common

Question: {4, 5, 6} ∩ {8, 9. 10}

Answer: Ø

Unions of Sets:

“What is the union of these sets?” is the same question as “What is the complete list of all the elements contained in both sets altogether?”

Note: If an element appears in both sets, it does NOT need to be listed twice in the union set.

Question: {p, a, r, k} U {d, r, i, v, e}

Answer: {p, a, r, k, d, i, v, e}

Notice in the answer that the element r is only listed once in the answer.

Question: {2, 4, 5, 7} U {1, 3, 5}

Answer: {1, 2, 3, 4, 5, 7}

Again, the element 5 is only listed once in the answer.

Negative Properties and Algebraic Expressions

1. Simplify: 6 + 4 [ 7 – (x – 2 )]

2. Simplify: - (x2 – 3x + 9)

Modeling Real Data with Algebraic Formulas

In math, equations are often generated to help model real life data. Often, these equations (also called formulas) help us to predict future data values.

For example, here are some Gray Wolf Population Totals (rounded to the nearest hundred) provided by the U.S. Department of the Interior:

U.S. Gray Wolf Population

800 900 1300 1700 2300 2500

Year 1960 1970 1980 1990 2000 2003

If P is the population of gray wolves in the U.S. and x is the number of years after 1960, this formula attempts to model the real data from the table:

P = 0.72x2 + 9.4x + 783

3. Use the formula to find the gray wolf population in the year 2000.

4. How well does this number match the real data from the table?