MATH 1044 Lecture Notes - Lecture 4: Plastic Bottle, Inflection
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And introduce the concept of a limit. The notions of direction, concavity and limit, as we will see, are three indispensable tools in deter(cid:373)i(cid:374)i(cid:374)g (cid:272)ertai(cid:374) properties of fu(cid:374)(cid:272)tio(cid:374)"s. Whe(cid:374) (cid:449)e talk of the dire(cid:272)tio(cid:374) of a fu(cid:374)(cid:272)tio(cid:374)"s graph, (cid:449)e (cid:373)ea(cid:374) (cid:449)hether it is (cid:373)o(cid:448)i(cid:374)g up or do(cid:449)(cid:374) as we increase the size of the input (i. e. move right along the input/horizontal axis). If the graph of a function is moving down, then the function is decreasing, i. e. the output values are getting smaller as the input values get larger. If the graph of a function is moving up, then the function is increasing, i. e. the output values are getting larger as the input values get larger. If the graph of a function is flat (horizontal), then the function is decreasing, i. e. the output values are not changing as the input values get larger. A function can be increasing on some parts while constant or decreasing on others.
