RULES FOR FUNCTIONSLINEAR OR NON-LINEAR

4 3 2 1 0In addition to level 3.0 and beyond what was taught in class, the student may: Make

connection with other concepts in math.

Make connection with other content areas.

 

The student will understand and explain the difference between functions and non-functions using graphs, equations, and tables. Compare

properties of a function to a non-function.

The student will be able to model and evaluate functions and non-functions. Use graphs,

equations, and tables to determine functions and non-functions.

 

With help from theteacher, the student has partial success with level 2 and 3 elements.

Even with help, students have no success with the functions.

Focus 6 - Learning Goal #1: Students will understand and explain the difference between functions and non-functions using graphs, equations, and tables.

CHARACTERISTICS OF LINEAR FUNCTIONS

A linear function is a relation between two variables which creates a straight line when graphed.

The equation or rule will not have exponents greater than 1.

Examples of linear functions:

y = 2x + 1

y = -1/2x – 5

y = -4x – 2.8

y = x + 9

Tell the person next to you the characteristics

of a linear function.

CHARACTERISTICS OF NON-LINEAR FUNCTIONS

A non-linear function is a relation between two variables that does not create a straight line when graphed.

The equation or rule could have one of the following traits:

An exponent greater than one.

A variable in the denominator.

Examples of non-linear functions: y = 3x2 + 2x + 5

y = -5x3

y = 8/x

y = -2.5x4 – 3x2 + 9x – 1.4

Tell the person next to you the characteristics of a non-linear

function.

LINEAR OR NON-LINEAR

1. y = 7x + 12

2. y = 2x2 – 5x + ¼

3. y = x3

4. y = 5/2 x – 1

5. y = 18/x + 4

1. Linear

2. Non-linear

3. Non-linear

4. Linear

5. Non-linear

WRITE A FUNCTION TO REPRESENT THE DATA IN THE TABLE.

Look at the x values. You need to know if they are going up by one or if they are skipping. (It’s easier to determine the rule if they are going up

by one.)

Next look at the y values. How are they changing? Are they going up by the same amount?

Are they going up by different amounts?

The y values in this table are going up one every time. That means the you will multiply each “x” by one.

WRITE A FUNCTION TO REPRESENT THE DATA IN THE TABLE.

Go back to the first x. After you multiply it by one, what do you need to do to make it equal the y value?

You need to add 4. This means the rule could be y = (1)x + 4

Once you decide on a rule, make sure it works for the other x values.

The function is y = x + 4.

WRITE A FUNCTION TO REPRESENT THE DATA IN THE TABLE.

Look at the x values. You need to know if they are going up by one or if they are skipping.

Next look at the y values. How are they changing? The y values in this table are going up five every

time. That means the you will multiply each “x” by five.

Go back to the first x. After you multiply it by five, what do you need to do to make it equal the y value?

You need to add 3. This means the rule could be y = (5)x + 3

Once you decide on a rule, make sure it works for the other x values.

The function is y = 5x + 3.

X Y

-2 -7

-1 -2

0 3

1 8

WRITE A FUNCTION TO REPRESENT THE DATA IN THE TABLE.

Look at the x values. You need to know if they are going up by one or if they are skipping. **They are going up by 2.**

Next look at the y values. How are they changing?

The y values in this table are going down 10 for every two x values.

That means the you will multiply each “x” by negative five.

Go back to the first x. After you multiply it by -5, what do you need to do to make it equal the y value?

You need to add 20. This means the rule could be y = (-5)x + 20

Once you decide on a rule, make sure it works for the other x values.

The function is y = -5x + 20.

X Y

1 15

3 5

5 -5

7 -15

9 -25

WRITE A FUNCTION TO REPRESENT THE DATA IN THE TABLE. Look at the x values. You need to know if they are going up by

one or if they are skipping.

Next look at the y values. How are they changing?

The y values in this table are changing by different amounts. This means that this is not linear. It will be exponential.

Choose one of the x values. Think about how you could square or cube the x to get close to the y value. 2 squared is close to 5, 3 squared is close to 10, 4 squared

is close to 17.

It looks like if we square the x value and add 1 we would have the w value. This means the rule could be y = x2 + 1

Once you decide on a rule, make sure it works for the other x values.

The function is y = x2 + 1.

X Y

0 1

1 2

2 5

3 10

4 17

5 26