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This guide covers essential concepts in mathematics related to functions and graphs, focusing on domain and range, even and odd functions, and piecewise functions. The domain consists of all x-coordinates, while the range includes all y-coordinates of a graph. It explains interval and set notation along with the proper use of brackets and parentheses. Additionally, you'll learn the characteristics of even and odd functions, as well as how to work with composite and piecewise functions through examples.
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Domain and Range • Domain – all of the x-coordinates of a graph • Range – all of the y-coordinates of a graph • Notation • Interval notation • Set Notation • Proper use of brackets & parentheses
Even/Odd Functions • A function is even if f(-x) = f(x) • Ex: f(x) = x2 • Also look at graph • Symmetric about y-axis • A function is odd if f(-x) = -f(x) • Ex:f(x) = x3 • Symmetric about origin
Piecewise Functions • Two functions with restricted domains that create a new graph. • Ex:
Composite Functions • Doing multiple operations with multiple functions. • Ex.: If g(x) = x2 and f(x) = x – 7, then what is f(g(2))?