1. Characteristics of Functions

2. Intercepts
x-intercept – the point at which the line intersects the x-axis at (x, 0)
y-intercept – the point at which the line intersects the y-axis at (0, y)

3. Finding the Intercepts
On a graph, just look at where the function is crossing the x-axis, and then the y-axis.
If you are given the equation:
Plug in 0 for y and solve for x: this is the x intercept
Plug in 0 for x and solve for y: this is the y intercept
-3x + 2y = 12

5. Interval Notation
Represents an interval as a pair of numbers. The numbers are the endpoints of the interval. Parentheses and/or brackets are used to show whether the endpoints are excluded or included

7. Trend of the Graph
Sweep from left to right and notice what happens to the y-values
Increasing goes up (L to R)
Decreasing falls down (L to R)
Constant is a horizontal graph

12. Continuous Data -has NO breaks & is measured
-is data that can take any value (within a range)
Examples: A person's height: could be any value (within the range of human heights), not just certain fixed heights; Time in a race: you could even measure it to fractions of a second

13. Discrete Data -has gaps or breaks & is counted
-can only take certain values
Example: the number of students in a class (you can't have half a student).

15. Extrema
Minimum Point – least value of the function Maximum Point –greatest value of the function

17. Set Notation
Using inequalities to describe the values

18. Domain & Range Domain – all x-values of a function
Range – all y-values of a function

22. Asymptote
A line that a graph gets closer and closer to, but never crosses or touches

25. The graph below represents Maria’s distance from home one day as she rode her bike to meet friends and do a couple of errands for her mom before returning home.
What do the horizontal lines on the graph represent?
Where in the graph shows her taking care of the 2 errands?
Compare how she traveled at the beginning to how she traveled at the very end.
Create Maria’s story so that it matches the graph.

26. Characteristics Domain: Range: Intercepts: Increasing or Decreasing?
Maximum or Minimum?

27. Characteristics Domain: Range: Intercepts: Increasing or Decreasing?
Maximum or Minimum?

28. Characteristics Domain: Range: Intercepts: Increasing or Decreasing?
Maximum or Minimum?
Horizontal Asymptote:

29. Characteristics Domain: Range: Intercepts: Increasing or Decreasing?
Maximum or Minimum?
Horizontal Asymptote:

35. Characteristics of Functions
Homework
Characteristics of Functions