Overview
The session covered how to find the domain and range from graphs, along with the concept of monotony and determining whether a function is even or odd.
Finding Domain and Range from the Graph
- The domain is all the X values that can be substituted into the function.
- The range is all the Y values resulting from the function.
- At a point, the domain is the X value and the output is the range.
- The domain is taken from the X-axis, and the range from the Y-axis.
- A straight line or continuous curve means domain and range over intervals.
- Open points (hollow circles) mean the value is not included (open interval).
- Closed points (filled circles) mean the value is included (closed interval).
- If the graph extends infinitely, we use infinity or negative infinity.
- The domain or range can be expressed as R except for excluded values.
Types of Segments in the Graph and Their Expression
- A line with a start and end is a line segment.
- A line with a start but no end is a ray.
- A line with no start or end is a straight line.
- In curves, if there is no arrow, it is not extended infinitely.
How to Write Domain and Range
- When there are missing points (holes), we use difference: R - {excluded values}.
- Intervals are written using parentheses: ( ) for open intervals, [ ] for closed intervals.
Notes When Dealing with Graphs
- Pay attention to holes and exclude those values.
- When expressing intervals, the smaller number is on the left and the larger on the right.
- Disconnected sets of values may be expressed using union between intervals.
Concept of Monotony
- Monotony determines if the function increases, decreases, or is constant.
- We move from left to right on the X-axis.
- Each increase or decrease interval is written as an open interval.
- If intervals differ (increase/constant/decrease), topics are divided according to change intervals.
Determining if the Function is Even or Odd from the Graph
- Even function: the right side of the Y-axis looks exactly like the left.
- Odd function: what happens above on the right happens inversely below on the left.
- If there is no exact match or symmetry: Neither even nor odd.
Key Terms & Definitions
- Domain (ุงูุฏูู
ูู) โ the set of X values that can be substituted into the function.
- Range (ุงูุฑูุฌ) โ the set of Y values resulting from the function.
- Interval (ุงููุชุฑุฉ) โ a part of the number line between two numbers.
- Open/Closed Interval (ูุชุฑุฉ ู
ูุชูุญุฉ/ู
ุบููุฉ) โ indicates whether the boundary is included or not.
- Monotony (ู
ููุชููู) โ the behavior of the function (increase/decrease/constant) over intervals.
- Even function (ุฏุงูุฉ ุฒูุฌูุฉ) โ the function is symmetric about the Y-axis.
- Odd function (ุฏุงูุฉ ูุฑุฏูุฉ) โ the function is symmetric inversely about the origin.
Action Items / Next Steps
- Solve all workbook questions: finding domain, range, and monotony for all graphs.
- Determine if the function is even, odd, or neither.
- Submit the assignment on Saturday.