1. Algebra 1 Ch 1.7 – Introduction to Functions

2. Objective  Students will identify functions and make an input/output table for a function

3. Functions  A relationship where one thing depends upon another is called a function.  A function is a rule that establishes a relationship between two quantities called the input and output.  In a function each input has exactly one output. More than one input can have the same output

4. Identifying Functions  The key to identifying functions is the rule that each input has exactly one output.  If an input has more than one output…then the data is not a function  Often times you will be given a table or a list of ordered pairs be asked to identify if the data is a function.  Let’s look at some examples…

5. Identifying Functions  Look at the table to the right…notice that each input has exactly one output…  Therefore, this set of data is considered a function InputOutput 53 64 75 86

6. Identifying Functions  Look at the table to the right…notice that the input of 9 has two different outputs (5 and 4 respectively)  Therefore, this set of data is not considered to be a function InputOutput 95 94 83 72

7. Identifying Functions  Look at the table to the right…notice that the input of 1 and 2 have the same output of 3  In this instance this is considered a function because each input has exactly one output…it’s ok to have different inputs with the same output InputOutput 13 23 34 44

8. Creating Input/Output Tables  You can create an input/output table by substituting given values into the rule and putting the results in a table  Let’s look at an example  Suppose you are asked to create an input/output table for the equation y = 3x + 2 using the values of 0, 1, 2, and 3.  Simply substitute the values of 0, 1, 2 and 3 into the equation for x and then figure out what y is equal to.

9. Comments  To get the desired results (input/output table) it really important that you are organized here…  We will use the methodology that we have previously learned about evaluating equations to determine the output.  That is… 1. Write the equation 2. Substitute 3. Simplify  Let’s continue with our example…

10. Example 1. y = 3x + 2 InputOutput y = 3(0) + 2 y = 0 + 2 y = 2 2. y = 3x + 2 y = 3(1) + 2 y = 3 + 2 y = 5 3. y = 3x + 2 y = 3(2) + 2 y = 6 + 2 y = 8 4. y = 3x + 2 y = 3(3) + 2 y = 9 + 2 y = 11 0 1 2 3 2 5 8 11

11. Comments  On the next couple of slides are some practice problems…The answers are on the last slide…  Do the practice and then check your answers…If you do not get the same answer you must question what you did…go back and problem solve to find the error…  If you cannot find the error bring your work to me and I will help…

12. Your Turn – Identifying a Function  Does the table represent a function? Explain InputOutput 13 14 25 36 InputOutput 11 23 36 410 InputOutput 13 26 311 418 InputOutput 59 48 39 27 1. 2. 3. 4.

13. Your Turn – Creating an Input/Output Table  Make an input/output table for each function. Use 0, 1, 2, 3 as the domain (output). 5. y = 21 – 2x 6. y = 5x 7. y = 6x + 1 8. y = 2x + 1 9. y = x + 4 10. y = 3x

14. Your Turn Solutions 1 Function 2 Function 3 Function 4 Not a Function # 5 – 10 lists the outputs only. The inputs should be 0, 1, 2, 3 5. 21, 19, 17, 15 6. 0, 5, 10, 15 7. 1, 7, 13, 19 8. 0, 3, 5, 7 9. 4, 5, 6, 7 10. 0, 3, 6, 9

15. Summary  A key tool in making learning effective is being able to summarize what you learned in a lesson in your own words…  In this lesson we talked about functions and creating function tables… Therefore, in your own words summarize this lesson…be sure to include key concepts that the lesson covered as well as any points that are still not clear to you…  I will give you credit for doing this lesson…please see the next slide…

16. Credit  I will add 25 points as an assignment grade for you working on this lesson…  To receive the full 25 points you must do the following: Have your name, date and period as well a lesson number as a heading. Do each of the your turn problems showing all work Have a 1 paragraph summary of the lesson in your own words  Please be advised – I will not give any credit for work submitted: Without a complete heading Without showing work for the your turn problems Without a summary in your own words…