Functions Patterns and Proportional Relationships Direct and Indirect

Functions, Patterns and Proportional Relationships Direct and Indirect Proportions

Function ¡A function is like a machine ¡ It has an input (x-value) and an output (y-value) ¡ For every input, there is exactly ONE output ¡ A function can be displayed by a rule, a table or graph. Function Introduction Video

Function 1 y=5 x - 1 Input Rule Output x 5 x – 1 y -2 0 3 6

Function 2 y=-2 x 2 Input Rule Output x -2 x 2 y -2 2 3 4

Can you find the pattern? Input (x) Output (y) 1 4 2 6 3 8 4 5 6 1. Complete the table 2. Can you write the function?

Graph the Function Y=x÷ 4 Input Rule Output Ordered Pair X X÷ 4 Y (x, y) -4 0 2 4

Describing Functions X 1 2 3 4 y 9 18 27 36 “As x increases by 1, y increases by _____”

Direct Proportion ¡ ¡ Any function that can be written in the form y=kx, where K is a constant EXAMPLE: y= 9 x When one number increases, the other number also increases X 1 2 3 4 y 9 18 27 36

Direct Proportion Example ¡ David earns $15 each hour he works for his grandmother doing odd jobs around the house. X (hours worked) Y ($ made) 1 2 3 4

Direct Proportion Example X (hours worked) 1 2 3 4 Y ($ made) $15 $30 $45 $60 Let x stand for the number of hours David worked and let y stand for the number of dollars she earns: Y= ___

Direct Proportion Y= 15 x ¡ A direct proportion exists! $$ made ¡ Hours worked

Direct Proportions in graphs ¡ ¡ To determine whether a line is the graph of a direct proportion, follow this rule: If a straight-line graph passes through the point (0, 0), it is the graph of a direct proportion

Which line is the direct proportion? n m

Indirect Proportion ¡ ¡ When two numbers are multiplied and the answer is a constant (k) EXAMPLE: xy=k y= k x For (1, 8), xy = ______ For (2, 4), xy = ______ For (4, 2), xy = ______ For (8, 1), xy = ______

Indirect Proportion

Thinking it Through ¡ Is the function y=3 x + 3 a direct proportion?

Thinking it Through ¡ Is the function y=3 x + 3 a direct proportion? Step 1: Pick a point If x = 1, y = ____ Y= X _______

Thinking it Through ¡ Is the function y=3 x + 3 a direct proportion? Step 3: Pick another point If x=3, y= ______ Y= X _______

Thinking it Through ¡ Is the function y=3 x + 3 a direct proportion? Another Way: Direct Proportions must pass through (0, 0) SO…when x=0, does y=0? ? ?

Hints for Proportion Questions ¡ Numbers being multiplied? ? It’s a Direct Proportion! ¡ Numbers being divided? ? It’s an Indirect Proportion!

Hints for Proportions ¡ Graph a straight line, going through (0, 0)? ? It’s a Direct Proportion! ¡ Graph a curve? ? It’s an Indirect Proportion!

Question 1 ¡ Which describes the equation y = 50/x ? Direct proportion b. Indirect proportion C. Neither a.

Question 2 ¡ a. b. c. Which statement describes the equation y = 10 x ? Direct proportion Indirect proportion Neither

Question 3 ¡ The Willy Wonka Factory can make 2, 000 chocolate bars per hour. This means there is a direct proportion between the number of hours the factory is operating and _______________.

¡ COACH l Pg. 154 l Pg. 158 l Pg. 162