LINEAR AND NON LINEAR FUNCTIONS

Lesson Three

Say if the following is a function or not. Justify your answer.

Which ordered pair is a solution to the function y = 1/3x – 5?a.(- 5, 3)b.(- 4, 3)c. (3, - 5)d.(3, - 4)

Describe the difference between a relation and a function.

Consider the following set of ordered pairs. Explain whether or not it is a function.(2, 3), (0,6) (- 4, 9) (5, -1)

WARM UP

Today in your groups you will work through a set of 4 problems. You will need to read each problem carefully. Each problem will pose a few questions. Answer the questions to the best of your ability. You may want to use a table and graph to help you answer the questions.

Let’s see what your group came up with. Be ready to share what your group discussed and discovered.

We will be going through the problems together. As we do this, look at what your group recorded and if you need to, make necessary corrections.

On Monday you put one penny in a jar. On Tuesday you put two pennies in the jar. On Wednesday you put four pennies in the jar. On Thursday you put eight pennies in the jar. You continue this pattern for many more days.

You are having a candlelight dinner. At 5.00 pm you light the beautiful tall candle. At 5.30 pm you notice the candle is 2.5 cm shorter. At 6.30 pm you notice that the candle is 5 cm shorter than it was at 5.30 pm. At 8.00 pm you find that the candle is 15 cm shorter than the original.

You can make bubble solution by mixing 1 cup of liquid soap with 4 cups of water.

A certain function fits the following description: “As the value of x increased by 1 each time, the value of y decreases by the square of x.”

Take a few minutes to write a sentence or two about what your group discovered. Use what we discussed as a class to help you if you need to.

Now, take turns going around your group and discuss what you have written. Come up with a common statement that you can share with the rest of the class.

From your investigation, can you now explain how you would define a linear function and an non-linear function?

Let’s think of real world examples that would show linear lines and non-linear lines.

A linear function is a function in which the graph of the solutions forms a straight line. Therefore, an equation of the form y = mx + b is a linear function.

A function can be considered continuous or discrete. Continuous data can take on any value, so there is no space between data values for a given domain. Discrete data have space between possible data values. Graphs of continuous data are represented by a solid line and graphs of discrete data are represented by dots.

Nonlinear functions are functions whose rates of change are not constant. Therefore, their graphs are not straight lines.

Let’s think about continuous graphs. Can you list examples of continuous graphs? 1.

2.

3.

Let’s think about discreet graphs. Can list examples of discreet graphs?1.

2.

3.

CLASSWORK

Work independently to complete the worksheet on linear and non-linear functions.

If you need additional assistance, ask your elbow partner. If your elbow partner cannot help you, ask me for help.

Record your answers on your worksheet.

Ticket out the door……..Look at the following graphs. Are they linear or non-linear. Justify your answer.

Explain how you would decide if a function is linear from a table.Is the following linear on non-linear?X 1 2 3 4 5

y 4 16 32 64 128

HOMEWORK

Tonight’s homework is from your workbook.

Complete Pg 331 #s 1 – 4 and Pg 332 #s 9 - 12