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Analyzing Graphs of Functions: Zeros, Maxima, and Minima

Explore domain, range, zeros, and behavior of functions with Relative Maxima and Relative Minima concepts. Learn how to identify odd or even functions and calculate average rate of change. Verify algebraically for f(x) = 0.5 - 3x.

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Analyzing Graphs of Functions: Zeros, Maxima, and Minima

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  1. Chapter 1: Lesson 1.5Analyzing Graphs of Functions Domain: All possible inputs (x) of a relation. Range: All possible outputs (y) of a relation. HW #9

  2. Vertical Line Test A relation is a function if no vertical line intersects the graph of the relation at more than 1 point. See page 50

  3. Finding the Zeros (or roots) Zeros or roots are also called x-intercepts if they are real numbers. All x-intercepts are zeros…or roots, but not all zeros are x-intercepts. The zeros of a relation are the x-values that make f (x) = 0.

  4. Describing Function Behavior See page 52 HW #33

  5. Relative Minima and Relative Maxima This is best handled visually on page 53

  6. Average Rate of Change For the interval of x = 1 to x = 5

  7. Odd, Even, or Neither Even Functions: Visually symmetric about the y-axis. f(-x) = f(x) (x, y) → (-x, y) Odd Functions: Symmetric with respect to the origin. f(-x) = -f(x) (x, y) → (-x, -y) Graph and determine whether the function is odd, even, or neither, Verify algebraically. #78 f(x) = 5 – 3x

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