NAME:



NAME: ____________________________________________________

INVESTIGATION 5A

FUNCTIONS

THE BASICS

HOMEWORK PACKET

In Functions- The Basics, you will explore function rules. Functions are like machines. Functions take something in (input) and give something out (output) according to certain rules.

[pic]

Name ________________________________ Date ___________

5.1 Homework Algebra

Sasha and Tony play the Guess My Rule game. Sasha’s rule is pick a number, add [pic], double your answer, subtract 3, and find half the result.

1. For each of Tony’s inputs below, what output does Sasha’s rule produce.

|a. 4 |b. 5 |

|c. 6 |d. -4 |

|e. -5 |f. -6 |

2. For each of Sasha’s responses below, what input did Tony give?

|a. 4 |b. 5 |

|c. 6 |d. -4 |

|e. -5 |f. -6 |

3. Find a simpler rule that does the same thing as Sasha’s rule.

Name _____________________________ Date ___________________

5.2 Homework Algebra 1

1. Convert hours to minutes. Round each answer to the nearest tenth of a minute.

a. 3 h b. 3.05 h c. 4.1 h d. 1.35 h e. 2.43 h

f. Write a rule (a description in words is fine) for converting hours to minutes.

2. Convert seconds to minutes. Round each answer to the nearest hundredth of a minute.

a. 9 s b. 37 s c. 71 s d. 105 s e. 279 s

f. Write a rule (a description in words is fine) for converting seconds to minutes.

3. Decide whether each of the following descriptions represents a function. Explain.

a. The input is a page number of The Scarlet Letter. The output is the number of words on that page.

b. The input is the area of a square. The output is the perimeter of that square.

c. The input is the area of a rectangle. The output is the perimeter of that rectangle.

4. Antonio signs up for a charity run. His sponsors can donate either a fixed amount or an amount of money based on the number of miles that he runs. The table shows the amount that each of Antonio’s sponsors will donate.

To Calculate now much money he will raise, Antonio makes this table

[pic]

a. Complete the table.

b. Write a rule that tells the total amount of money Antonio will raise based on how many miles he will run.

c. If he runs 7 miles, how much money will Antonio make?

d. How many miles must Antonio run to raise $50? To raise $100? Round up your answer to the nearest mile.

Name ___________________________ Date ________________

5.3 Homework Algebra 1

1. Determine whether each rule defines a function. If it does, make a table of output values using integer inputs from 0 to 4. If it does not, explain.

a. Take the opposite of the input and then add 2.

b. Square the input and then subtract 4.

c. [pic]

d. x produces a number that is 4 units away from x on the number line.

2. Modeling situations as functions is common. Decide whether each description represents a function. Explain.

a. The input is a day of the year. The output is the average temperature in Barcelona on that day.

b. The input is the speed of a car. The output is the time it takes for a car moving constantly at that speed to travel 100 miles.

c. The input is a year. The output is the population of the United States during that year.

3. For each description in Exercise 2, reverse the description for input and output. Which new descriptions result in functions? Explain.

4. Dana’s favorite number is 5. She invents five different rules shown below.

[pic]

a. Show that each rule fixes 5. In other words, show that when the number 5 is the input, the number 5 is also the output.

b. Pick any whole number between 2 and 10 (except 5). Change Dana’s rules so that the new rules fix the number you choose.

c. Show that your five new rules fix the number you choose.

Name _______________________________ Date ________________

5.4 Homework Algebra 1

1. Use these four functions for parts (a) – (e)

[pic]

a. Hideki chooses one of these functions. When he uses the number 5 as the input, the output is 14. Can you tell which function he is using? Explain.

b. Hideki puts in a 0 and gets back a 1. Can you tell which function he is using? Explain.

c. Hideki says, ”The input I chose this time gives the same output for function f and j.” Which input did he choose?

d. What input(s), if any, give the same outputs for function g and for function j?

2. Suppose you drive on a straight road at 30 miles per hour. Model this situation using a function that converts driving time into distance traveled.

3. Dorothy describes the following number trick. Pick a number. Multiply it by 3. Add 5. Double it. Add 8. Divide by 6. Subtract the original number. Dorothy always tells your ending number.

a. Choose at least 5 different numbers as inputs for Dorothy’s function. Write the input-output pairs in a table.

b. Input x into Dorothy’s rule. Apply each step in Dorothy’s rule to x and record each step. What is the final result?

4. Use the functions [pic] and [pic]. Evaluate each function.

a. g(0), g(1), and g(-1) b. h(0), h(1), and h(-1)

c. g(3) + 5 d. g(4) + h(4)

5. Let m represent a function that uses two points as inputs and gives back a number as an output. The two input points are [pic] and [pic].

[pic]

a. What does the output m(P, Q) represent?

b. Calculate m(P, Q) when P is (-1, 2) and Q is (2, 6)

Name ___________________________ Date ___________________

5.5 Homework Algebra 1

1. What is the domain of [pic]?

2. Use the function rule “Divide the input by 3 and write the remainder.”

a. Make an input-output table with integer inputs between 1 and 5.

b. Is the value 0 a valid input? Is a negative integer a valid input? Explain.

3. When [pic], which of the four values is missing in the table?

A. -4 B. -2

C. 4 D. 6

Decide whether each graph is the graph of a function. Explain.

4. 5.

6. A resort charges $50 plus $10 per person to rent a cabin for a day.

a. Write a rule to calculate the total cost of renting a cabin for a day.

b. Use your rule to find the total cost for six people to stay in a cabin for a day.

7. Use the functions to find the value.

[pic]

a. f(7) b. g(7) c. h(7)

Name _______________________________ Date ________________

5.6 Homework Algebra 1

1. Graph each function

2. Which graph of a function has a maximum value of 10?

3. Elaine explains how she finds fixed inputs, or inputs that remain unchanged by a function. “Let’s say you want to find a value fixed by the rule [pic]. First, graph [pic]. Then, graph y = x. The graphs intersect at (3, 3). See! The rule [pic]fixes the value 3.”

Use Elaine’s method to find fixed inputs for each function in Exercise 1. Does her method work?

4. Use the functions p and q given below.

[pic]

a. Make an input-output table for each function. Use at leas five inputs. Are the tables the same?

b. Are the valid inputs for each rule the same?

c. Graph each function. Illustrate your answers for parts (a) and (b) on your graphs.

5. Decide whether each graph is the graph of a function.

[pic]

6. Larissa selects mobile phone service. Each company charges a fixed monthly fee plus an additional charge for each minute in excess of the free time allowance.

[pic]

Larissa plans to use her mobile phone as her only phone. She predicts that she will use it between 600 and 900 minutes per month. To find t, the total monthly charge for each company based on m minutes of phone use, Larissa writes the equations below.

[pic]

Which is the less expensive plan for 600 minutes of phone use per month?

A. Company A B. Company B

C. Both plans cost the same amount for 600 minutes. D. Cannot be determined.

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