Coordinate Algebra Mr. Do Combining Functions Coordinate Algebra Mr. Do

Objectives SWBAT identify like terms SWBAT add and subtract like terms SWBAT multiply terms SWBAT combine functions

Like Terms Like terms are terms in an expression that have the same variable raised to the same power. Constants are considered to be like terms.

Like Terms Like Terms: 2 conditions Must have the same variable Circle the like terms Variables must have same exponent Circle the like terms

Combining Like Terms Combining terms means to add or subtract like terms.

Combining Like Terms Example Combine like terms 1. 5x2 – x + 8 + 6x – 10 + 2x2

Quick Check! Combine like terms 1. 3x2 - 7x + 3x +10 – 8 – 2x2 2. 7y2 + 4 - 9y -3y +3y2 3. 2xy2 + 8x2y - 5x2y + 5xy2

Multiplying Terms 3 steps Multiply numerical coefficients together List all the variables that occur in the terms being multiplied Add the exponents of like variables

Multiplying Terms Examples Multiply the terms 1. 6(x5) 2. 5x2(3x6) 3. (7x3y6)(2x8y3) 4. (4x3)(2x2 - 4x + 3x6)

Quick Check! Multiply the terms 1. 2x2(-4x3) 2. 7(3x2) 3. (3x10y)(5x3y3) 4. (2x4)(5x + 3x4 - x6)

Tarsia Puzzle Match the appropriate sides to form a large triangle

Combining Functions Example 1 If f(x) = 2x + 4 and g(x) = 3x - 7, find f(x) + g(x)

Combining Functions Example 2 If f(x) = 6x2 - 3x + 5 and g(x) = 4x2 + 5x - 8, find g(x) - f(x)

Combining Functions Example 3 If f(x) = 5x2 - 3, find 6f(x).

Combining Functions Example 4 If f(x) = 4x2 + 2 and g(x) = 3x2, find g(x)•f(x).

Guided Practice

Independent Practice

Ticket out the Door If f(x) = 2x2 + 2 and g(x) = 6x2, Find 3f(x) Find f(x) – g(x) Find g(x)•f(x)