Lesson 4-3: Patterns and Non-Linear Functions 4-3.1 – Classifying functions as linear or non-linear Vocabulary: Non-Linear Function – A function whose graph is not a line or part of a line Just like linear functions, non-linear functions can be represented using words, tables and graphs. For example: If you were opening a pizzeria, you could have various sizes of pizzas according to the chart below: Pizza Type Radius (in) Area Personal 2 12.57 Small 4 50.27 Medium 6 113.10 Large 8 201.06 X-Large 10 314.16 This would be a non-linear relationship because the graph between the radius and the area does not form a straight line. However, if you look at the sauce needed for the pizzas and relate that to the cost as in the next chart: Weight (oz) Cost 2 $0.80 4 $1.60 6 $2.40 8 $3.20 10 $4.00 Then the cost of the sauce and the mount used for each pizza is linear.
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Lesson 4-3: Patterns and Non-Linear Functions
4-3.1 – Classifying functions as linear or non-linear
Vocabulary:Non-Linear Function – A function whose graph is not a line or part of a line
Just like linear functions, non-linear functions can be represented using words, tables and graphs.
For example: If you were opening a pizzeria, you could have various sizes of pizzas according to the chart below:
Pizza Type Radius (in) AreaPersonal 2 12.57
Small 4 50.27Medium 6 113.10
Large 8 201.06X-Large 10 314.16
This would be a non-linear relationship because the graph between the radius and the area does not form a straight line.
However, if you look at the sauce needed for the pizzas and relate that to the cost as in the next chart:
Then the cost of the sauce and the mount used for each pizza is linear.
You also have to cut the pizza into slices. The number of cuts relates to the number of slices as shown below.
Pizza SlicesCuts 1 2 3 4Slices 2 4 6 8
4.3-2 – Representing Patterns and Non-Linear functions
The table shows the total number of block that makes up a cube as a function of the number of blocks on one edge.
Edge Size Total Blocks1 12 83 374 ?5 ?
Find the pattern, and you will see that the total number of blocks is the edge cubed, so 4 would be 43∨64 and 5 would be 53∨125. It would be non-linear.
The equation would be y=3x
4.3-3 – Writing a rule to describe a non-linear function
The order pairs (1 ,2 ) , (2 ,4 ) , (3 ,8 ) , (4 ,16 ) ,∧(5 ,32) represent a function. What is the rule to represent this function.
Rules that could get you from 1 to 2 would be y=2x , y=x+1∧ y=2x. The first two do not work for each of the others but the last one works for all three pairs. So y=2x is the equation for the function.
What would the rule for the function represented by the ordered pairs (1 ,1 ) , (2 ,4 ) , (3 ,9 ) , (4 ,16 )∧(5 ,25)
