1. RULES FOR FUNCTIONS LINEAR OR NON-LINEAR

2. 43210 In 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 the teacher, 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.

3. 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 / 2 x – 5  y = -4x – 2.8  y = x + 9 Tell the person next to you the characteristics of a linear function.

4. 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 = 3x 2 + 2x + 5  y = -5x 3  y = 8 / x  y = -2.5x 4 – 3x 2 + 9x – 1.4 Tell the person next to you the characteristics of a non-linear function.

5. LINEAR OR NON-LINEAR 1. y = 7x + 12 2. y = 2x 2 – 5x + ¼ 3. y = x 3 4. y = 5 / 2 x – 1 5. y = 18 / x + 4 1. Linear 2. Non-linear 3. Non-linear 4. Linear 5. Non-linear

6. 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.

7. 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.

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.  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. XY -2-7 -2 03 18

9. 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. XY 115 35 5-5 7-15 9-25

10. 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 = x 2 + 1  Once you decide on a rule, make sure it works for the other x values.  The function is y = x 2 + 1. XY 01 12 25 310 417 526