FIND THE PATTERN RULE IN A TABLE WORKSHEET

Part A :

For the following input numbers and output numbers, find the rule in the number crunching machine :

Problem 1 :	Solution
Problem 2 :	Solution
Problem 3 :	Solution
Problem 4  :	Solution
Problem 5 :	Solution
Problem 6 :	Solution

Part B :

For each of the following tables, write a formula connecting the variables. 

Check your formula for all the number pairs given :

Problem 1 :	Solution
Problem 2 :	Solution
Problem 3 :	Solution
Problem 4 :	Solution
Problem 5 :	Solution
Problem 6 :	Solution

Given the following output numbers and rules, calculate the corresponding input numbers :

Example 1 :

Rule : the input number plus four

Output numbers  {5, 7, 15}

Solution

Example 2 :

Double the input number plus two

Output numbers  {2, 4, 10}

Solution

Example 3 :

Rule : Five times the input number minus three

Output numbers {7, 12, 17}

Solution

Example 4 :

Rule : Add one to the input number then double the result 

Output numbers  {2, 6, 12}

Solution

Example 5 :

Rule : Multiply the input number by itself then add one

Output numbers : {2, 5, 17}

Solution

Example 6 :

Rule : Multiply the input number by one more than itself.

Output numbers {2, 6, 20}

Solution

Example 7 :

A farmer sells potatoes and tomatoes in a market. During the day, he gets 3 customers.

• The first customer demands 2 kg of potatoes and 1 kg of tomatoes.
• The second customer demands 1 kg of potatoes and 2 kg of tomatoes.
• The third customer demands 5 kg of potatoes and 2 kg of tomatoes.
• The price of potatoes per kg is $30 and the price of tomatoes per kg is $20.

a) Draw the input-output table for the given situation and find the revenue earned by the farmer from each customer and the total revenue.

b) Formulate a  mathematical expression to show the relationship between the price of potatoes and tomatoes, the quantities sold and the revenue.

c) If a fourth customer visits his shop and demands 3 kg of potatoes and 2 kg of tomatoes, calculate the total revenue earned by the farmer using the mathematical equation formulated in question b.

Solution

Problem 1 :

Let f(x) = 3x + 2. Find the values of the following.

(i) f(1)

(ii) f(-2)

(iii) f(⁻¹⁄₃)

(iv) f(½)

Solution

Problem 2 :

Let g(x) = -2x + 5.

Find the values of the following.

(i) g(-1)

(ii) g(3)

(iii) g(⁻¹⁄₂)

(iv) g(¼)

Solution

Problem 3 :

Let h(x) = (½)x + 5.

Find the values of the following.

(i) h(-2)

(ii) h(0)

(iii) h(4)

(iv) h(1)

Solution

Problem 4 :

Let f(x) = 2x - 1.

Find the value of x for the given value of f(x).

(i) f(x) = 13

(ii) f(x) = -3

(iii) f(x) = 0

(iv) f(x) = ½

Solution

Problem 5 :

Let g(x) = -3x + 4.

Find the value of x for the given value of f(x).

(i) g(x) = 1

(ii) g(x) = -5

(iii) g(x) = 0

(iv) g(x) = ½

Solution

Problem 6 :

Let h(x) = (⁻²⁄₃)x + 5.

Find the value x for the given value of h(x).

(i) h(x) = 7

(ii) h(x) = 0

(iii) h(x) = -1

(iv) h(x) = ⁻¹⁄₂

Solution

Problem 7 :

f(x) = 3x + b

In the function above, b is a constant. If f(2) = 8, find the value of f(-1).

Solution

Problem 8 :

Let f(x + 3) = -7x + 5. Find the value of f(2).

Solution

Problem 9 :

A house security company is charging house owner a onetime setup fee $175 plus y dollars for each month of monitoring the house. Find the function which models the total charge for 12 months. And also, find the total charge, if the monthly charge is $15.

Solution

Problem 10 :

A taxi service charges a flat rate of $20 plus $3.25 for each mile travelled. Write a function which represents the total charge for x number of miles travelled. And also, find the total charge for 40 miles travelled.

Solution

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.