1. How do we interpret and represent functions? F.IF.6 Functions Lesson 3.3 Identifying key features of a graph

2. Identifying Key Features of a Graph Intercepts: X-intercept: The place on the x-axis where the graph crosses the axis

3. Identifying Key Features of a Graph Intercepts: y-intercept: The place on the y-axis where the graph crosses the axis

4. Identifying Key Features of a Graph Intercepts: Find the x and y intercepts of the following graph. 1. ?

5. Identifying Key Features of a Graph Increasing or Decreasing???? Increasing: A function is said to increase if while the values for x increase as well as the values for y increase. (Both x and y increase)

6. Identifying Key Features of a Graph Increasing or Decreasing???? Decreasing: A function is said to decrease if one of the variables increases while the other variable decreases. (Ex: x increases, but y decreases)

7. Identifying Key Features of a Graph Intervals: An interval is a continuous series of values. (Continuous means “having no breaks”…it keeps going.) A graph is Discrete if it “has breaks”…it stops

8. Continuous vs. Discrete ContinuousDiscrete

9. Identifying Key Features of a Graph Intervals:  A function is positive when its graph is above the x-axis.  The function is negative when its graph is below the x-axis.

10. Identifying Key Features of a Graph The function is positive when x > ? When x > 4!

11. Identifying Key Features of a Graph Extrema:  A relative minimum is the point that is the lowest, or the y-value that is the least for a particular interval of a function.  A relative maximum is the point that is the highest, or the y-value that is the greatest for a particular interval of a function.  Linear and exponential functions will only have a relative minimum or maximum if the domain is restricted

12. Example 1 What is the relative minimum? Relative maximum?

13. Example 2 What is the relative minimum? Relative maximum?

14. Identifying Key Features of a Graph Domain and Range: Domain: all possible input values Range: all possible output values

15. Example 1 What is the domain? Range?

16. Example 2 What is the domain? Range?

17. Remember your numbers when describing domain and range… Natural numbers: 1, 2, 3,... Whole numbers: 0, 1, 2, 3,... Integers:..., –3, –2, –1, 0, 1, 2, 3,... Rational numbers:numbers that can be written as a fraction, terminating decimal or repeating decimal – ¾,.875, 1/3, … Irrational numbers: numbers that cannot be written as a fraction, terminating decimal or repeating decimal – 3.141592…, 1.414213…, etc. Real numbers: the set of all rational and irrational numbers

18. Identifying Key Features of a Graph Asymptotes: A line that the graph gets closer and closer to, but never crosses or touches. -Sometimes drawn on the graph via a dashed line. -Never on Linear Functions. y = -4

19. Example 1 Identify the asymptote:

20. Example 2 Identify the asymptote:

21. Identifying Key Features of a Graph Guided Practice Example 1 A taxi company in Atlanta charges $2.75 per ride plus $1.50 for every mile driven. Determine the key features of this function. Identify the following: 1.Type of function (linear/exponential) 2.Continuous or Discrete 3.Intercepts (x and y) 4.Increasing or Decreasing 5.Intervals (positive/negative) 6.Extrema 7.Domain and Range 8.Asymptotes if any

22. Guided Practice: Example 1, continued Identify the type of function described. – We can see by the graph that the function is increasing at a constant rate. – The function is linear.

23. Guided Practice: Example 1, continued 2.Identify the intercepts of the graphed function. – The graphed function crosses the y-axis at the point (0, 2.75). – The y-intercept is (0, 2.75). – The function does not cross the x-axis. – There is not an x-intercept.

24. Guided Practice: Example 1, continued 3.Determine whether the graphed function is increasing or decreasing. – Reading the graph left to right, the y-values are increasing. – The function is increasing.

25. Guided Practice: Example 1, continued 4.Determine where the function is positive and negative. – The y-values are positive for all x-values greater than 0. – The function is positive when x > 0. – The y-values are never negative in this scenario. – The function is never negative.

26. Guided Practice: Example 1, continued 5.Determine the relative minimum and maximum of the graphed function. – The lowest y-value of the function is 2.75. This is shown with the closed dot at the coordinate (0, 2.75). – The relative minimum is 2.75. – The values increase infinitely; therefore, there is no relative maximum.

27. Guided Practice: Example 1, continued 6.Identify the domain of the graphed function. – The lowest x-value is 0 and it increases infinitely. – x can be any real number greater than or equal to 0. – The domain can be written as x ≥ 0.

28. Guided Practice: Example 1, continued 7.Identify any asymptotes of the graphed function. – The graphed function is a linear function, not an exponential; therefore, there are no asymptotes for this function.

29. On Your Own Identify the following: 1.Type of function (linear/exponential) 2.Continuous or Discrete 3.Intercepts (x and y) 4.Increasing or Decreasing 5.Intervals (positive/negative) 6.Extrema 7.Domain and Range 8.Asymptotes if any