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Understanding Graphs of Functions: Domain, Range, and Zeros

Learn how to analyze graphs of functions, find domain and range, zeros, identify intervals of increase and decrease, and recognize relative minima and maxima. Explore step and piecewise defined functions as well as even and odd functions.

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Understanding Graphs of Functions: Domain, Range, and Zeros

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  1. 2.3 Analyzing Graphs of Functions

  2. Graph of a Functionset of ordered pairs

  3. Look at the graph of p. 201 Find domain range f(-1) f(2)

  4. Vertical Line Test If a vertical line intersects the graph more than once, the graph is not a function

  5. Zeros of a Function: x values when Find the zeros of the following functions

  6. Increasing and Decreasing Functions Increasing Decreasing Constant

  7. Linear Function Graph:

  8. Ex. Write a linear function where

  9. Relative Minimum and Relative Maximum A function value f(a) is called a relative minimum of f if there exists an interval (x1, x2) that contains a such that A function value f(a) is called a relative maximum of f if there exists an interval (x1, x2) that contains a such that

  10. Step Functions and Piecewise Defined Functions Greatest Integer Function: - the greatest integer less than or equal to x.

  11. Piecewise Defined function

  12. Even and Odd Functions • Even symmetric to y axis • Odd symmetric about origin

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