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Lecture Notes 2.4 MAT 109 2.4 Functional Notation and Piecewise Functions Objectives for Section 2.4: Write the difference quotient for a function in simplest form for which f(x) = 0, or f(x) <0, or f(x) > 0 Evaluate functions using functional notation Find function values and graphs for piecewise functions Read from a graph of a function f the domain, range, function values, and values of x A useful notation commonly used with functions allows us to represent more conveniently the value of the dependent variable for a particular value of the independent variable. In this notation a letter such as fis used to name a function, and then an equation such as y = 2x + Sis written as f(x) = 2x + 5. The dependent variable y is replaced by f(x), with the independent variable x appearing in parentheses. The expression f(x) is read “f of x” or “f at x” and means the value of the function (the y value) corresponding to the value of x. Similarly, (7) is read “f of 7” or “f at 7” and means the function value when x = 7. To find f(7) in this example, we substi- tute 7 for xin the equation f(x) = 2x + 5. f(x) = 2x +5 — Given equation. (7) = 2(7) +5 Replace x by 7. = 19 Simplify. The result f(7) = 19 says that when x = 7, y = 19. Example 1: Using Functional Notation Ify = f(x) =2x* x44, find a) f(2), b) f(15), and c) f(—3). Example 2 If the value V of a particular work of art is given by the function V = f(x) = 50,000(1.07), where x is the number of years since its purchase at $50,000, then find and interpret /(9).
