1. Warm Up
Evaluate f(x) = 4x – 7 over the domain {1, 2, 3, 4}. What is the range?

2. How do we interpret and represent functions. F. IF
How do we interpret and represent functions? F.IF.6 Functions Lesson 3: Identifying key features of a graph

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

4. Example 1
Identify the x-intercepts:

5. Example 2
Identify the x-intercepts:

6. Example 3
Identify the x-intercepts:

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

8. Example 1
Identify the y-intercepts:

9. Example 2
Identify the y-intercepts:

10. Example 3
Identify the y-intercepts:

11. Identifying Key Features of a Graph1.
Intercepts: Find the x and y intercepts of the following graph. ?

12. 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)

13. 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)

14. Example 1
Increasing or decreasing?

15. Example 2
Increasing or decreasing?

16. Identifying Key Features of a Graph
Intervals: An interval is a continuous series of values. (Continuous means “having no breaks.)

17. 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.

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

19. Example 1 Part 1
The function is positive when x _ __?

20. Example 1 Part 2
The function is negative when x _ __ ?

21. Example 2 Part 1
The function is positive when x _ __ ?

22. Example 2 Part 2
The function is negative when x _ __ ?

23. 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

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

25. 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 Irrational numbers: numbers that cannot be written as a fraction, terminating decimal or repeating decimal Real numbers: the set of all rational and irrational numbers

26. Example 1
What is the domain? Range?

27. Example 2
What is the domain? Range?

28. Identifying Key Features of a Graph
Asymptotes: A line that the graph gets closer and closer to, but never crosses or touches.

29. Example 1
Identify the asymptote:

30. Example 2
Identify the asymptote:

31. Identifying Key Features of a Graph
Identify the following:
Type of function
Domain and Range
Increasing or Decreasing
Extrema
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.

32. Identifying Key Features of a Graph
Guided Practice
Example 2:
Identify the following:
Type of function
Domain and range
Increasing or decreasing
Asymptote