Concavity
This
lesson will teach students what concavity is and what it looks like on a graph.
Also, I will go over how the graph of a line can be increasing and decreasing
at the same time that it is concave up or down.
The graph of a linear
function is a straight line because the average rate of change is constant. But,
not all graphs of functions are straight lines, they can be bent upwards or
downwards. This upwards and downwards is called concavity.
- · A graph that is bent upward is concave up.
- · A graph that is bent downwards is concave down.
The graph of a line can also be increasing or decreasing at
the same time that it is concave up or down.
- · A graph is increasing when the line is rising from left to right.
- · A graph is decreasing when then line is falling from left to right.
EXAMPLES OF CONCAVITY UP/DOWN AND INCREASIND/DECREASING
 |
| Concave Up / Increasing |
 |
| Concave Up / Decreasing |
 |
| Concave Down / Decreasing |
 |
| Concave Down / Increasing |
Photos taken from:
http://www.biology.arizona.edu/biomath/tutorials/functions/Properties.html
The graphs you chose are a great illustration of concavity. You explained when a graph is either concave up or concave down and you also discussed when it is increasing or decreasing. Good point about the rate of change affecting the graph.
ReplyDeleteThe graphs you provided are really helpful in explaining concavity
ReplyDeleteThe graphs perfectly describe increasing, decreasing, concave up and concave down! good job!
ReplyDeletemilana,
ReplyDeletereally great lesson! your images really helped support your explanation of concavity. i really like how you compared lines with curves to differentiate what concavity looks like. a real world example using this concept would have been a great addition, but still great job!
professor little
larry@mail.postmanllc.net
ReplyDeletegreat examples, graphs and tables!
ReplyDelete^^
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