HOW TO TELL IF AN ARROW DIAGRAM IS A FUNCTION

If each input associates with one output, then it is a function.

Tell whether the relation is a function. Explain.

Problem 1 :

Solution :

The relation is a function.  Because each input value is paired with only one output value.

Problem 2 :

Solution :

The relation is a function.  Because each input value is paired with only one output value.

Problem 3 :

Solution :

The relation is not a function. Because input 5 has associated with more than one output -4 and -3. So, it is not a function.

Problem 4 :

Solution :

The relation is a function. 

Because, there are four input values (-8, -4, 0 and 4). But no values is associated more than one output.

Tell whether the relation is a function. Explain.

Problem 5 :

Solution :

The relation is a function.  Because each input value is paired with only one output value.

Problem 6 :

Solution :

The relation is not a function.  Because 1 is paired with more than one output value (both -1 and 2).

Problem 7 :

Joe buys DVDs at $15 each. He has enough money to buy at most 3 DVDs. Write a function to describe the situation.

Find a reasonable domain and range of the function

Solution :

Cost of each DVD = $15

Maximum number of DVD's can be purchased = 3

Let x be the number of DVD's

Amount spent = 15x

When x = 0

f(0) = 15(0)

= 0

Domain = {0, 1, 2, 3} 

Range = {0, 15, 30, 45}

Problem 8 :

Bill puts his glass of water into the refrigerator. The water’s temperature starts at 76^oF, but drops 2 degrees every minute until it reaches the refrigerator’s temperature of 36^oF. Write a function to describe the situation. Find a reasonable domain and range of the function

Solution :

After x minutes, the temperature will be

t(x) = 76 – 2x degrees Fahrenheit

The temperature needs to drop 40 degrees, so it will take 20 minutes. The temperature is dropping continuously, so write the domain and range using inequalities.

Reasonable domain: 0 ≤ x ≤ 20

Reasonable range: 36 ≤ y ≤ 76

Problem 9 :

A car rental company charges $10 an hour (a part of an hour rounds up to the next hour) to rent a car. The limit to the number of hours you can rent the car is 8 hours.

a. Write a rule in function notation for this situation. f(x) = 10x

b. What is a reasonable domain and range for this situation?

Solution :

Domain: {0, 1, 2, 3, 4, 5, 6, 7, 8}

x = 8

f(8) = 10(8)

= 80

Range: {0, 10, 20, 30, 40, 50, 60, 70, 80}

Problem 10 :

The American Sycamore tree grows approximately 6 feet per year until they reach a maximum height of about 66 ft.

a. Write a rule in function notation for this situation. f(x) = 6x

b. What is a reasonable domain and range for this situation?

Solution :

f(x) = 6x

a)

The American Sycamore tree grows approximately 6 feet per year and it reach its maximum height of 66 ft.

When f(x) = 66

6x = 66

x = 66/6

b)

Domain: 0 ≤ x ≤ 11

Range: 6 ≤ y ≤ 66

Problem 11 :

Mary earns $8 per hour proofreading advertisements for a local newspaper. She works 5 hours per day.

a. Write a rule in function notation for how much Mary earns.

f(x) = 8x

b. What is a reasonable domain and range for this situation?

Solution :

Domain: {0, 1, 2, 3, 4, 5}

Range: {0, 8, 16, 24, 32, 40}

Problem 12 :

Ms. Bolus was born 22 inches long and grew approximately 3 inches per year until she reached a maximum height of 5’1’’.

a. Write a rule in function notation for Ms. Bolus’ growth.

f(x) = 3x + 22

b. What is a reasonable domain and range for this situation?

Solution :

Domain: 0 ≤ x ≤ 13

Range: 22 ≤ y ≤ 61

Problem 13 :

The fastest marathon runner averages 13 miles every hour. A marathon is 26.2 miles total.

a. Write a rule in function notation for the situation.

f(x)= 13x

b. Find a reasonable domain and range of the function.

Solution :

Domain: 0 ≤ x ≤ 2.01538

Range : 0 ≤ y ≤ 26.2

Problem 14 :

Pedro is making chocolate chip cookies. He has a bag of chocolate chips that contains 150 chocolate chips. He is very particular about his cookies, so he makes sure that there are exactly 15 chocolate chips in each cookie.

a. Write a rule in function notation to calculate the number of chocolate chips left in the bag.

f(x) = 140 – 15x

b. Find a reasonable domain and range of the function.

Solution :

Domain: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

Range: {5,20, 35, 50, 65, 80, 95, 110, 125, 140 }