For more information, please see full course syllabus of Pre Algebra

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For more information, please see full course syllabus of Pre Algebra

For more information, please see full course syllabus of Pre Algebra

### Functions

- A function is a relationship that gives each input value exactly one output value.
- A function rule is the equation that describes a function. You substitute the input value and use the equation to determine the output value.
- Write a function notation by creating an equation in the form f(x) = y. x is the input value and y is the output value.

### Functions

Half of the toys made at a certain toy factory are blue. Use the function rule b = 0.5t to make a table of input t and output b pairs using t = 4, 20, 98.

- b = 0.5t
- b(4) = 0.5 ×4
- b(4) = 2
- b(20) = 0.5 ×20
- b(20) = 10
- b(98) = 0.5 ×98
- b(98) = 49

Input (t) | Output (b) |

4 | 2 |

20 | 10 |

98 | 49 |

You are going to the store to buy peaches to bake a pie. The peaches cost $ 3.50 per pound. Write an equation to represent the total cost for buying p pounds of peaches. Then evaluate the cost of buying 5 pounds of peaches.

- Let c = cost for buying p pounds of peaches.
- c = $ 3.50p
- c(5) = $ 3.50 ×5

c(5) = $ 17.50

You start with $ 18. You earn $ 20 while working at your summer job. Write a function to show the relationship between the total amount of money you have and the amount of money you earn at your job.

- Let t = total amount of money you have.

t = $ 18 + $ 20

Complete the table by evaluating the given function: y = 4x + 1.

Input (x) | Output (y) |

-2 | |

1 | |

3 | |

5 |

- y( − 2) = 4( − 2) + 1 =
- − 8 + 1 =
- − 7
- y(1) = 4(1) + 1 =
- 4 + 1 =
- 5
- y(3) = 4(3) + 1 =
- 12 + 1 =
- 13
- y(5) = 4(5) + 1 =
- 20 + 1 =
- 21

Input (x) | Output (y) |

-2 | -7 |

1 | 5 |

3 | 13 |

5 | 21 |

Complete the table and find the rule for the function.

Input (x) | Output (f(x)) |

-5 | 2 |

-3 | 4 |

0 | 7 |

2 | |

4 |

- The rule for the function is f(x) = x + 7

Input (x) | Output (f(x)) |

-5 | 2 |

-3 | 4 |

0 | 7 |

2 | 9 |

4 | 11 |

Ice cream costs $ 2.40 plus $ 0.50 for each topping added. Write a function that describes the relationship between the number of toppings and the total cost. Then find the cost if you get 4 toppings.

- Let x = number of toppings, and f(x) = total cost.
- f(x) = $ 2.40 + $ 0.50x
- When you get 4 toppings, x = 4
- f(4) = $ 2.40 + $ 0.50(4)
- f(4) = $ 2.40 + $ 2.00

f(4) = $ 4.40

A cell phone plan sells you 500 minutes a month for $ 20.50. Each additional minute costs $ 0.05.

Write a function representing the relationship between your phone bill and the number of minutes you use.

Then find the cost of your phone bill if you used 537 minutes this month.

Write a function representing the relationship between your phone bill and the number of minutes you use.

Then find the cost of your phone bill if you used 537 minutes this month.

- Let x = number of minutes over 500.
- f(x) = cost of 500 minutes + cost of additional minutes
- f(x) = $ 20.50 + $ 0.05x
- If you use 537 minutes, you used 37 additional minutes, so x = 37
- f(37) = $ 20.50 + $ 0.05(37)
- f(37) = $ 20.50 + $ 1.85

f(37) = $ 22.35

Use the function f(x) = 9 − 2x to fill out the following input and output table.

Input (x) | Output (f(x)) |

-3 | |

-1 | |

0 | |

4 | |

5 |

- f( − 3) = 9 − 2( − 3)
- f( − 3) = 9 + 6
- f( − 3) = 15
- f( − 1) = 9 − 2( − 1)
- f( − 1) = 9 + 2
- f( − 1) = 11
- f(0) = 9 − 2(0)
- f(0) = 9 − 0
- f(0) = 9
- f(4) = 9 − 2(4)
- f(4) = 9 − 8
- f(4) = 1
- f(5) = 9 − 2(5)
- f(5) = 9 − 10
- f(5) = − 1

Input (x) | Output (f(x)) |

-3 | 15 |

-1 | 11 |

0 | 9 |

4 | 1 |

5 | -1 |

A pair of socks costs $ 1.75, and a scarf costs $ 4.80. Write a function describing the total cost, the number of pairs of socks you buy, and the number of scarves you buy. What is the total cost if you buy 2 pairs of socks and 3 scarves?

- Let c = total cost, p = number of pairs of socks, and s = number of scarves.
- c = $ 1.75p + $ 4.80s
- c = $ 1.75(2) + $ 4.80(3)
- c = $ 3.50 + $ 14.40

c = $ 17.90

Dog treats cost $ 1.25 each, and cat treats cost $ 0.75. You buy 3 dog treats and 5 cat treats. Write a function describing the relationship between the number of cat treats you buy, the number of dog treats you buy, and the total cost. What is your total cost?

- Let t = total cost, d = number of dog treats, and c = number of cat treats.
- t = $ 1.25d + $ 0.75c
- t = $ 1.25(3) + $ 0.75(5)
- t = $ 3.75 + $ 3.75

t = $ 7.50

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Functions

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- What You'll Learn and Why 0:04
- Topics Overview
- Vocabulary 0:24
- Function
- Function Rule
- Evaluating a Function Rule 0:59
- Example: Table of Input and Output
- Using Function Notation 2:56
- Example: Write the Equation and Evaluate the Cost
- Writing Functions 4:40
- Example: Writing Function
- Extra Example 1: Complete the Table 6:02
- Extra Example 2: Complete the Table and Find the Function 7:38
- Extra Example 3: Function Notation 9:39
- Extra Example 4: Write a Function and Find the Total Cost 11:49

0 answers

Post by Manzoor Shah on April 9, 2014

This became Crystal Clear after I watched this.

0 answers

Post by Aurrora Greening on September 28, 2011

does it matter what order the addition is put in a function? for example the yogurt question, yo write the equation C= 3.95 + 0.5t, is it incorrect to write the function C= 0.5t + 3.95?

0 answers

Post by amin khalif on September 25, 2011

to easy