Section 1.2. Function A function from a set D to a set R is a rule that assigns a unique element in R to each element in D. In this definition, D is the.

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Presentation transcript:

Section 1.2

Function A function from a set D to a set R is a rule that assigns a unique element in R to each element in D. In this definition, D is the domain of the function and R is a set containing the range. Which of these is a function???

Function Here is a handout with the “Twelve Basic Functions” from Pre-Calculus. Know these very well!!!

Domain and Range  The domains and ranges of many real-valued functions of a real variable are intervals or combinations of intervals. The intervals may be open, closed or half-open, finite or infinite.  The endpoints of an interval make up the interval’s boundary and are called boundary points.  The remaining points make up the interval’s interior and are called interior points.

Domain and Range  Closed intervals contain their boundary points.  Open intervals contain no boundary points

Domain and Range

Find the domain and range of the given functions, both analytically and graphically.

Domain and Range Find the domain and range of the given functions, both analytically and graphically. Beware of grapher failure with this one…

Even and Odd Functions  The graph of an even function is symmetric about the y-axis. A point (x, y) lies on the graph if and only if the point (  x, y) lies on the graph.  The graph of an odd function is symmetric about the origin. A point (x, y) lies on the graph if and only if the point (  x,  y) lies on the graph.

Even and Odd Functions Determine whether the given functions are even, odd, or neither. Answer without showing any work, but be prepared to explain how you arrived at your answers. Even Neither Even What could you change about any of these functions to make them odd?

Graphs of Piecewise Functions Graph (0, 0) (1, 1)

Composite Functions

Find a formula for, then find