1. Lesson 4-6 Relations

2. Transparency 6 Click the mouse button or press the Space Bar to display the answers.

3. Transparency 6a

4. Objectives Determine whether a relation is a function Find function values

5. Vocabulary Function – a relation where each domain value is paired with exactly one range value Vertical line test – a vertical line touches a function only in one place Function notation – f(x) read as f of x: range value = f(domain value)

6. Function Slide TableGraphMapping Set of ordered pairs: {(3,2), (5,3), (4,3), (5,2)} XY 32 53 43 52 y x 345345 2323 xy

7. Example 1 A. Determine whether the relation is a function. Explain. Answer: This is a function because the mapping shows each element of the domain paired with exactly one member of the range.

8. Example 1 cont B. Determine whether the relation is a function. Explain. Answer: This table represents a function because the table shows each element of the domain paired with exactly one element of the range. xy –7–12 –4–9 2–3 50 C. Determine whether {(–5, 2), (–2, 5), (0, 7), (0, 9)} is a function. Explain. Answer: This relation is not a function because the element 0 in the domain is paired with both 7 and 9 in the range.

9. Example 2 Determine whether x = -2 is a function. Graph the equation. Since the graph is in the form the graph of the equation will be a line. Place your pencil at the left of the graph to represent a vertical line. Slowly move the pencil to the right across the graph. At this vertical line passes through more than one point on the graph. Answer: The graph does not pass the vertical line test. Thus, the line does not represent a function.

10. Example 3 A. If find. Multiply. Subtract. Answer: Replace x with 4. B. If find. Multiply. Subtract. Answer: Replace x with –5.

11. Example 3 cont C. If find. Distributive Property Simplify. Answer: Replace x with 2 – x.

12. Example 4 A. If, find. Multiply. Simplify. Answer: Replace m with –3. B. If, find. Simplify. Answer: Replace m with 6z.

13. Summary & Homework Summary: –A relation is a function if each element of the domain is paired with exactly one element of the range –Substitute values for x to determine f(x) for a specific value Homework: –pg 229-30: 18-42 even