Unit 4: Introduction to Functions

1. Unit 4: Introduction to Functions Topic: Writing & Graphing Functions

2. Instructions for taking PPT notes • Play the PowerPoint presentation (either download it to your laptop or play it directly from the website). • Take notes in the “Notes” section of your binder as you view the presentation (use the note taking style with which you are most comfortable). REMEMBER: Taking notes doesn’t mean copying EVERYTHING in the presentation word for word; paraphrase, abbreviate, etc. • Have your textbook open to the related sections (from your calendar) & use those sections to supplement the information in the presentation. • Do NOT simply print the PowerPoint & bring it to class; this would have a negative effect on your journal grade.

3. Journal Entries • Any time the words “JOURNAL ENTRY” appear in the presentation, you should do the following: • In your math journal, write the title & date at the beginning of your entry. • Respond to the prompt.

4. Writing functions • Writing a function from data: • Look for patterns in the relationship between x & y. • Ex. {(1, 3), (2, 6), (3, 9), (4, 12)} • In each coordinate point, y is 3 times bigger than x, so y = 3x. • Ex. • For each column in the table, y is 3 less than x, so y = x – 3.

5. Writing functions • Writing a function from a word problem: • Identify independent and dependent variables. • Identify any constants, and the operator(s) associated with them. • Using variables and constants, write a function that relates the independent and dependent variables in a way that MAKES SENSE. • If necessary, identify a reasonable domain & range.

6. Writing functions • Ex. Erick charges $7 per hour for yard work. • Identify independent and dependent variables. • Ind: hours worked; Dep: money earned (the amount of money Erick earns DEPENDS on the number of hours he works). • Identify any constants, and the operator(s) associated with them. • 7, multiplication (“per hour” means to multiply number of hours). • Using variables and constants, write a function that relates the independent and dependent variables in a way that MAKES SENSE. • M = 7h; if Erick makes $7 every hour, the total hours (h) times 7 will equal the amount of money (M) earned. • If necessary, identify a reasonable domain & range. • D: h > 0, R: M > 0; the domain represents time, which cannot be negative (or 0, otherwise he did no work). The range will also be positive since he can’t earn negative dollars (or $0).

7. Evaluating Functions • Evaluate the function f(x) = 4x – 5 for x = 3 and x = -5. • Replace x in the function with each given value and simplify. • x = 3: f(3) = 4(3) – 5 = 12 – 5 = 7 • x = -5: f(-5)=4(-5) – 5 = -20 – 5 = -25

8. Graphing functions • Things to remember: • If you are not given specific domain values, determine a reasonable domain. • If the domain is all real numbers, make a table of values & choose domain values to find corresponding range values. Choose enough values to show a pattern when your points are graphed (don’t ignore negative #s). • Determine if the graph is discrete or continuous. • If the graph is continuous, connect the points with a line or curve. If the graph is discrete, do NOT connect the points. • If the domain is all real numbers, draw arrows to show the graph continues forever.

9. JOURNAL ENTRY • TITLE: Checking My Understanding: Writing & Graphing Functions • Review your notes from this presentation & create and complete the following subheadings in your journal: • “Things I already knew:” Identify any information with which you were already familiar. • “New things I learned:” Identify any new information that you now understand. • “Questions I still have:” What do you still want to know or do not fully understand?

10. Homework Textbook Section 4-3 (pg. 249): 8, 12-22, all, 24 Textbook Section 4-4 (pg. 256): 12-24, even; must use graph paper DUE 10/24 (A-day) or 10/25 (B-day)