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

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

3. 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.

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

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

6. Combining Like Terms Example Combine like terms
1. 5x2 – x x – x2

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

8. 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

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

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

11. Tarsia Puzzle
Match the appropriate sides to form a large triangle

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

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

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

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

16. Guided Practice

17. Independent Practice

18. 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)