Unit 2 Part 2 Special Functions

Size: px

Start display at page:

Download "Unit 2 Part 2 Special Functions"

Dorthy Murphy
5 years ago
Views:

1 Unit 2 Part 2 Special Functions Name: Piecewise Functions - Graphing Shipping Rates The following information comes from the United States Postal Service website, You will use your calculator to generate 5 random package weights, which you will place on the axes on the front board. To get your package weights: In the scratchpad on your calculator, choose MENU 5: Probablility 4: Random 6: Seed Enter your cell phone number and hit enter MENU 5: Probablility 4: Random 1: Number Bump out of the parentheses, multiply by 8, and hit enter 5 times Enter your 5 points into the class Desmos table: Weight Cost 1. What do you notice about our graph? 2. What do you wonder? 3. What characteristics of this graph are similar or different from graphs you ve seen before? What about the context causes these similarities/differences? 4. Is this relation a function? If so, state the domain and range. 1

2 Piecewise Functions Introduction 1) You have a summer job that pays time and a half overtime. That is, if you work more than 40 hours per week, your hourly wage for the extra hours is 1.5 times your normal hourly wage of $7. Number of Hours worked Money earned a) How much will you make if you work 35 hours? 40 hours? 45 hours? b) Write an expression for wages earned if you work up to 40 hours. c) Write an expression for waged earned if you work over 40 hours. d) Let s practice writing the piecewise function: 2

3 2) You and your friends decide to go to Detroit for a Red Wings game. You find a parking garage with the following rates: $2 per hour for the first 3 hours and $8 maximum for over 3 hours. a. Fill out the table b. Make a graph time cost time cost 0 2 hours 15 mins 2 hours 15 mins 30 mins 2 hours 30 mins 45 mins 2 hours 45 mins 1 hour 3 hours 1 hour 15 mins 4 hours 1 hour 30 mins 5 hours 1 hour 45 mins 6 hours c. How much would it cost to stay for 10 hours? When would the cost be exactly $2? Exactly $3? d. Let s see if we can write the piecewise function: Practice Evaluating Functions: Evaluate the function for the given value of x. 5x 1, if x < 2 2) f(x) = { x 9, if x 2 a) f(-4) b) f(-2) c) f(0) d) f(5) 3

4 2x, if x 1 3) h(x) = { x + 3, if x < 1 a) h(1) b) h(-10) c) h(6) d) h(0) Piecewise Functions Piecewise Function - Example: 1. Evaluate the function for the given value of x. 3x 1, if x 4 f(x) = { 2x + 7, if x > 4 a. x = 10 b. x = 4 c. x = -2 d. x = Evaluate the function for the given value of x. 5x 1, if x 1 f(x) = { x + 4, if x > 1 a. x = 1 b. x = 4 c. x = -2 d. x = 1 3 4

5 Rules for graphing a piecewise function: 1. Graph each equation, one at a time, over its specified domain. 2. If or, you will use a circle for the endpoints. If < or >, you will use a circle for the endpoints. Example: Graph the functions. f x 1 x 4, x 1 2 2x 3, x 1 2x 5, x 2 f x 3x 2, 2 x 1 2, x 1 x y x y x y x y x y 5

6 During a nine hour snowstorm it snows at a rate of 1 inch per hour for the first two hours, at a rate of 2 inches per hour for the next 6 hours, and a rate of 1 inch per hour for the final hour. a. Write and graph a piecewise function that gives the depth of the snow during the snowstorm. b. How many inches of snow accumulated from the storm? 6

7 Introduction to Absolute Value Graphs Card Sort Examine all of the graphs, tables, and equations you have. 1. What do all of the graphs have in common? 2. What do all of the equations have in common? 3. What do all of the tables have in common? Sort all of the graphs according to some commonality among the graphs. Find at least three different ways to sort the graphs. You have been provided with space for 4 different groupings, but you may only need 2 or 3 spaces, depending on your commonality. Sort #1 We grouped the following graphs together (give the letter of the graphs you grouped together): Grouping 1: Grouping 3: Grouping 2: Grouping 4: We grouped the graphs together, because Sort #2 We grouped the following graphs together (give the letter of the graphs you grouped together): Grouping 1: Grouping 3: Grouping 2: Grouping 4: We grouped the graphs together, because 7

8 Sort #3 We grouped the following graphs together (give the letter of the graphs you grouped together): Grouping 1: Grouping 3: Grouping 2: Grouping 4: We grouped the graphs together, because Absolute Value Functions Absolute Value: Plug the following values into the function and then plot the points. 1. y x x y x y ( x, y )

9 2. y x 3 2 x y x 3 2 y ( x, y ) General form of an absolute value equation: y a x h k Vertex: (, ) Slope: (Always go right first!) Example: Graph the functions. a. y x 2 3 b. y 2 x 1 4 ( h, k ) = ( h, k ) = 9

10 1 c. y x 2 3 d. y x ( h, k ) = ( h, k ) = Example: Write an absolute value equation for the graph shown. a. b. ( h, k ) = ( h, k ) = Equation: Equation: 10

11 c. d. ( h, k ) = ( h, k ) = Equation: Equation: Graph Linear Inequalities in Two Variables After completing the Desmos Polygraph, think about what characteristics of the graphs from the activity are similar or different from graphs you ve seen before. Were the graphs from the activity functions? Why or why not? If they were functions, state the domain/range. Linear inequality in two variables: replace the = sign in a linear equation with <., >, or. 11

12 Example 1: Determine whether the ordered pair is a solution of the inequality a. 3x 4y > 9 (2, 0) b. 2x + 3y 14 (5, 2) c. y 8 (-9, -7) Steps for graphing a linear inequality in two variables: Step 1: Put the inequality into a nice graphing formant, and then graph the boundary line. Use a line for < or > Use a line for or Step 2: Determine which side of the line to shade, and then shade that entire region. Shade the line for < or Shade the line for > or Example 2: Graph the inequality a. y < x + 4 b. y 3x

13 c. 2y + 4x > 8 d. x + 4y < - 8 e. y < 2 f. x 1 e. y > -2x + 3 f. x 4 13

1. Consider the following graphs and choose the correct name of each function.

Name Date Summary of Functions Comparing Linear, Quadratic, and Exponential Functions - Part 1 Independent Practice 1. Consider the following graphs and choose the correct name of each function. Part A: