MATH 1300 Lecture Notes - Lecture 5: Function Composition, Sine Wave

• School: York University
• Department: Mathematics and Statistics
• Course: MATH 1300
• Professor: Paul Skoufranis

Document Summary

Math 1300 lecture 5 notes new functions from old functions. Transformations of functions: by applying certain transformations to the graph of a given function we can obtain the graphs of related functions, this will give us the ability to sketch the graphs of many functions quickly by hand. It will also enable us to write equations for given graphs. 2sx , and y s2x : solution, the graph of the square root function y sx . In general, given any two functions f and t, we start with a number x in the domain of t and calculate tsxd. In other words, s f 8 tdsxd is defined whenever both tsxd and f stsxdd are defined: example. For s2 2 sx to be defined we must have. It is possible to take the composition of three or more functions. 1: so far we have used composition to build complicated functions from simpler ones.