- Finding patterns in shapes
- Finding the next terms of a geometric sequence with whole numbers
- Finding the next terms of an arithmetic sequence with whole numbers
- Identifying independent and dependent quantities from tables and graphs
- Writing an equation and drawing its graph to model a real-world situation: Basic
- Graphing ordered pairs and writing an equation from a table of values in context
- Writing and evaluating a function that models a real-world situation: Basic
- Finding outputs of a two-step function with decimals that models a real-world situation
- Finding outputs of a one-step function that models a real-world situation
- Interpreting a line graph
- Graphing a line in quadrant 1
- Writing a function rule given a table of ordered pairs: One-step rules
- Function tables with two-step rules
- Graphing whole number functions
- Making a table and plotting points given a unit rate
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Writing a function rule given a table of ordered pairs: One-step rules
In this lesson, we find the function rule given a table of ordered pairs.
We first identify the input and the output variables and their values. We find if the function is increasing or decreasing.
If the function is increasing, it means there is either an addition or multippcation operation between the two variables.
If the function is decreasing, it means there is either a subtraction or spanision operation between the two variables.
Consider the following table −
x | y |
---|---|
3 | 15 |
5 | 25 |
6 | 30 |
8 | 40 |
9 | 45 |
We see that the y values are increasing as the x values are increasing. So it is an increasing function. So, the variables x and y must be related either by addition or multippcation operation.
We check addition operation on x and y values as follows −
3 + 12 = 15
5 + 12 = 17
We check multippcation operation on x and y values as follows −
3 x 5 = 15
5 x 5 = 25 and so on
We see that the relation between x and y is a multippcation operation here and the constant for which all values are satisfied is 5.
So the function rule for this table of x and y values is “Multiply by 5”.
Consider another table −
x | y |
---|---|
10 | 13 |
15 | 18 |
19 | 22 |
23 | 26 |
28 | 31 |
Here we identify the input and output and then see the output y is increasing as input x is increasing.
13 = 10 + 3; 18 = 15 + 3; 22 = 19 + 3 and so on.
So, output y = input x + 3
Therefore, we identify the function rule here as “Add 3”.
Given the following table of ordered pairs, write a one-step function rule.
Input(x) | Output(y) |
---|---|
0 | 3 |
2 | 5 |
4 | 7 |
6 | 9 |
8 | 11 |
Solution
Step 1:
From the table 0 + 3 = 3; 2 + 3 = 5 and so on
Step 2:
Input + 3 = Output or x + 3 = y
Step 3:
Therefore the function rule here is ‘Add 3’ to the input to get the output.
Given the following table of ordered pairs, write a one-step function rule.
Input(x) | Output(y) |
---|---|
0 | 0 |
1 | 6 |
2 | 12 |
3 | 18 |
4 | 24 |
Solution
Step 1:
From the table 0 × 6 = 0; 1 × 6 = 6 and so on
Step 2:
Input × 6 = Output or x × 6 = y
Step 3:
Therefore the function rule here is ‘Multiply by 6’ the input to get the output.