February 29 th March 4 th

Transcription

1 February 29 th March 4 th Unit 7: Introduction to Functions

2 Jump Start Table A: Bags of candy ( ) Cost ( ) $1.25 $2.50 $3.75 $5.00 $6.25 $7.50 $8.75 $10.00 Table B: Number of seconds ( ) Distance traveled in feet ( ) a) Decide whether Table A and B are linear functions. b) Describe some differences between Table A and B *When functions can only have positive integers for the input, we call these functions... *When functions can have any input, we call these functions... 1

3 Comparing Linear Functions Example 1: Functions 1, 2, and 3 have the tables shown below. Examine each of them, make a conjecture about which will be linear, and justify your claim. Input Output Input Output Input Output Hint: If a relation is a linear function, the slopes between the points will always be the same. Slope can also be referred to as the rate of change. 2

4 Example 2: A function assigns the inputs and corresponding outputs shown in the table below. Input Output a. Is the function a linear function? Check at least three pairs of inputs and their corresponding outputs. b. What equation describes the function? c. What will the graph of the function look like? Explain. Independent Practice 1) Sylvie claims that the table of inputs and outputs below will be a linear function. Is she correct? Explain. Input Output

5 Reminders: To find the slope or rate of change when...» You have an equation in y = mx + b form,» A table,» A graph, Independent Practice Directions: Use your knowledge about calculating the rate of change (slope) to make comparisons about the following scenarios. 1. The graph below represents the distance,, Car A travels in minutes. The table represents the distance,, Car B travels in minutes. Which car is traveling at a greater speed? Explain. Car A: Car B: Time in minutes Distance

6 2. The rule =123 is used to describe the function for the number of minutes needed,, to produce toys at Toys Plus. Another company, #1 Toys, has a similar function that assigned the values shown in the table below. Which company produces toys at a slower rate? Explain. Time in minutes ( ) Toys Produced ( ) , , The local park needs to replace an existing fence that is 6 feet high. Fence Company A charges $7,000 for building materials and $200 per foot for the length of the fence. Fence Company B charges based on the length of the fence. That is, the total cost of the six-foot high fence will depend on how long the fence is. The table below represents the inputs and the corresponding outputs that the function assigns for Fence Company B. Input (length of fence) Output (cost of bill) 100 $26, $31, $46, $65,000 a. Which company charges a higher rate per foot of fencing? How do you know? b. *At what number of the length of the fence would the cost from each fence company be the same? What will the cost be when the companies charge the same amount? If the fence you need is 190 feet in length, which company would be a better choice? 5

7 Jump Start 1. A function has the table of values below related to the total cost for gallons of gas purchased. Number of gallons ( ) Total cost ( ) $19.71 $21.90 $54.75 $62.05 a. Determine if the function is linear. Explain why or why not. b. Is the function discrete or continuous? How do you know? c. What number does the function assign to 15? Explain what your answer means. Functions in Geometry Recall the following definitions from geometry... Perimeter Area Volume 6

8 Independent Practice Directions: Recall that the volume of a prism can be found using the equation, V = lwh. Use this formula to answer the questions that follow. 1) What is the volume of the rectangular prism shown below? 2) What is the volume of the rectangular prism shown below? 3) The volume of the prism shown below is 61.6 in 3. What is the height of the prism? 7

9 *Reminder: r = radius and is the line segment on a circle that goes from its center to the edge. 8

10 Independent Practice 1) What is volume of the right circular cylinder shown below? Round to the nearest tenth if necessary. 2) Use the diagram to find the volume of the right circular cone. Round to the nearest hundredth if necessary. 3) Use the diagram to find the volume of the right circular cone. Round to the nearest tenth if necessary. 9

11 4) Use the diagram to help you find the volume of the right circular cylinder. Round to the nearest hundredth if necessary. 5) Use the diagram to help you find the volume of the right circular cone. Round to the nearest hundredth if necessary. 6) Use the diagram to help you find the volume of the right circular cylinder. Round to the nearest tenth if necessary. 10

12 Jump Start 1) Determine whether the graph below represents a function or not. If it is a function, explain whether the function is linear or nonlinear. If it is not a function, explain why. 2) Determine whether the graph below represents a function or not. If it is a function, explain whether the function is linear or nonlinear. If it is not a function, explain why. 3) Determine whether the graph below represents a function or not. If it is a function, explain whether the function is linear or nonlinear. If it is not a function, explain why. 11

13 More Functions in Geometry Example 1: Compute the exact volume for the sphere shown below. Example 2: The average basketball has a diameter of 9.5 inches. What is the volume of an average basketball? Round your answer to the tenths place. Independent Practice 1) Use the diagram to find the volume of the sphere. Round your answer to the nearest hundredth. 12

14 2) A spherical fish tank has a radius of 8 inches. Assuming the entire tank could be filled with water, what would the volume of the tank be? Round your answer to the tenths place. 3) Use the diagram to answer the questions. a. Predict which of the figures shown above has the greater volume. Explain. b. Use the diagram to find the volume of each, and determine which has the greater volume. Round your answers to the nearest tenths. 13

15 4) Use the diagram to find the volume of the sphere. Round to the nearest hundredths. 5) Determine the volume of a sphere with diameter 9 mm, shown below. Round to the nearest tenths if necessary. 6) Which of the two figures below has the lesser volume? Round answers to the nearest tenths. 7) One of two half spheres formed by a plane through the sphere s center is called a hemisphere. What is the formula for the volume of a hemisphere? 14

16 Jump Start 1) Determine whether the graph below represents a function or not. If it is a function, explain whether the function is linear or nonlinear. If it is not a function, explain why. 2) Determine whether the graph below represents a function or not. If it is a function, explain whether the function is linear or nonlinear. If it is not a function, explain why. 3) Determine whether the graph below represents a function or not. If it is a function, explain whether the function is linear or nonlinear. If it is not a function, explain why. 15

17 Week 25 Homework 1) A function assigns the inputs and corresponding outputs shown in the table to the right. a. Is the function a linear function? Check at least three pairs of inputs and their corresponding outputs. Input Output b. What equation describes the function? c. What will the graph of the function look like? Explain. 2) Determine the volume of the rectangular prism shown below. 6.4 in. 5.1 in in. 16

18 3) Use the diagram to help you find the volume of the right circular cone. Round your answer to the nearest tenths. 4) Two people, Adam and Bianca, are competing to see who can save the most money in one month. Use the table and the graph below to determine who will save more money at the end of the month. Who is saving money at a faster rate? Adam s Savings: Bianca s Savings: Output Input (Total amount of (Number of Days) money) 5 $17 8 $26 12 $38 20 $62 17