Sample Page 7 | COMPASS REVIEW: FUNCTIONS
" ... Students will be able to determine whether or not a situation describes a function... to identify the domain and range of many functions, use function notation, and evaluate a function at specified values. They will determine whether or not two functions are equal on the domain of counting numbers...make a table and/or graph to represent a function, including step functions. They will write a function and create a simple program for the calculator to convert temperature scales (Celsius to Fahrenheit), write a linear or exponential growth function (involving compound interest or population growth) for real world situations and graph it on the coordinate plane. They will also graph a function on the calculator and use the TRACE feature to evaluate it at specific values. Given two or more functions, students will be able to find and evaluate a composite function...write a function as the composite of two or more simpler functions and describe some real world processes as composite functions..." |
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How Functions Function | |
| 6.4 Describing Functions With Algebra
Sometimes people describe a function as a "machine" or a "mystery box" like the one in Display 6.26 - you put a thing in, something happens to it, and some (related) thing comes out.
The point of this picture is not that a function is magic or mysterious, but that it's an "automatic" routine. Whenever you put a domain element into a function, the process automatically gives you one, and only one, image. It might take some (brain) power to run the machine, but there is no puzzle or uncertainty in the process. Once a thing is put in, exactly one result can come out. Viewed in this way, functions show you the power of using symbols for numbers. We work through a process once, mapping out what happens to a "typical" input (domain element) that is represented by a symbol. Then all we have to do is plug any number we want into the place of the input symbol, and we get the corresponding output without any further hard work. It becomes just a matter of routine, something that can be done over and over again in exactly the same way, without having to think much about it. The following example illustrates the power and efficiency of using algebra to describe a process in function form. Learning Outcomes After studying this section, you will be able to: Use any first degree equation of the form Find images of real numbers using linear functions and some functions of higher degree; Use a graphing calculator to draw graphs of linear functions and some functions of higher degree.
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