Writing a Function Rule

1. Writing a Function Rule

2. Independent and Dependent Variables • Independent Variable • Will change no matter what • The first member of the ordered pair • Domain • x • Dependent Variable • Changes depend on the independent variable • The second member of the ordered pair • Range • y

3. Independent and Dependent • y = 3x – 2 • Cost of three pounds of apples • Hours worked, amount paid • Weight of a book, number of pages • The circumference of a circle, the measure of the radius • The price of a single pair of shoes, the total price of 4 pairs of shoes • Number of hours spent typing a paper, length of paper • Time spent studying for a test, score on the test

4. Independent and Dependent-answers • y = 3x – 2 I = x, D = y • Cost of three pounds of apples I = # of apples D = Cost • I = Hours worked, D = amount paid • D = Weight of a book, I = number of pages • D = The circumference of a circle, I = the measure of the radius • I = The price of a single pair of shoes, D =the total price of 4 pairs of shoes • I = Number of hours spent typing a paper, D = length of paper • I = Time spent studying for a test, D = score on the test

5. Function Notation • You use the symbol f(x) in place of y • Function notation allows you to see the input value.

6. An Example • If f(x) = 2x + 8, find f(-2) • Replace x with –2 on the right and simplify: • f(-2) = 2(-2) + 8 • f(-2) = -4 + 8 • f(-2) = 4

7. Another Example • If g(a) = -3a – 5, find g(-1). • Replace a in the function rule with –1 and simplify. g(-1) = -3(-1) – 5 g(-1) = 3 – 5 g(-1) = -2

8. Using a Table of Values • You can write a rule for a function by analyzing a table of values. • Ask yourself “What did I do to the x-values to get the y-values?”

9. Another Way From a table • Find the differences between the values in the x column (independent variable) • Find the differences in the values in the y coulmn (dependent variable) • If there is a constant difference in each, divide the y differences by the x differences • That quotient will be the number multiplied by “x”

10. Another Way From a table • So you have y = x. What else do you have to do to that to get the number in the y column? (Usually add or subtract something.)

11. Steps to Write a Function • Find change in y values • Find change in x values • If constant for both – divide change in y by change in x • This is what you multiply x by • Figure out if you need to add or subtract something to get your y • Check another x value to make sure you are correct

12. 2 2 1 1 2 2 1 1 2 2 1 1 y = 1x ? y = 1x ? Tables of Values 2 ÷ 2 = 1 1 ÷ 1 = 1 y = x + 2 y = x + 10

13. Try these…

14. Try these…-answers f(x) = -x + 20 f(x) = 3x

15. Try these… • For f(x) = 4x – 9, find f(x) when x = 3 and x = 5. • For g(x) = 1/3x - 10 find g(27) and g(-15) • Identify the independent variable: The cost to wrap an order is $3 plus $1 per item wrapped. • Identify the dependent variable: Tabor charges $25 for each lawn he mows.

16. Try these…answers • For f(x) = 4x – 9, find f(x) when x = 3 and x = 5. 3 and 11 • For g(x) = 1/3x - 10 find g(27) and g(-15) • -1 and -15 • Identify the independent variable: The cost to wrap an order is $3 plus $1 per item wrapped. Number of items • Identify the dependent variable: Tabor charges $25 for each lawn he mows. Amount earned