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Understanding Functions, Domains, and Vertical Line Test

Learn about functions and domains, including how to find the domain of given functions and apply the Vertical Line Test to determine if a curve is a function. Discover Absolute Value and sketch its function. Analyze cost equations and functions.

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Understanding Functions, Domains, and Vertical Line Test

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  1. Function Definitions

  2. Finding the Domain • Domain is all x values for which f(x) exists • Example: Find the domain for each below a) f(x) = √(5 – x2) b) g(x) = (x2 – x – 6)/(x2 – x -2)

  3. Vertical Line Test • Used to determine is a curve is a function • A curve in the xy plane is a function of x if and only if no vertical line intersects the curve more than once

  4. Absolute Value • │a│ = a if a ≥ 0 • │a│ = -a if a < 0 • Sketch f(x) = │a│+ 1

  5. Find the formula of the function whose graph is shown

  6. Sketch the graph and find the domain and range f(x) = 1 – x2 x≤2 2x – 7 x>2

  7. The cost of mailing a first-class letter is 32 cents up to one ounce; plus 23 cents for each successive ounce up to 4 ounces. Is it a function? write and equation and graph

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