224 Chapter 2 Linear Equations in Two Variables and Functions Function Notation f (x) is the value of the function f at x. The domain of a function defined by y f (x) is the set of x-values that when substituted into the function produces a real number. In particular, • Exclude values of x that make the denominator of a fraction zero. • Exclude values of x that make the expression within a square root negative. Example 3 Given f (x) 3x2 5x, find f (2). f 122 31222 5122 12 10 22 Example 4 Find the domain. 1. f 1x2 x 4 x 5 ; Domain: 1, 52 ´ 15, 2 f 1x2 1x 3; Domain: 33, 2 2. 3. f 1x2 3x2 5; Domain: 1, 2 Section 2.7 Graphs of Functions Key Concepts A function of the form f 1x2 mx b 1m 02 is a linear function. Its graph is a line with slope m and y-intercept (0, b). f 1x2 k A function of the form is a constant function. Its graph is a horizontal line. A function of the form f 1a 02 1x2 ax2 bx c is a quadratic function. Its graph is a parabola. Examples Example 1 f 1x2 f1x2 3 2x 3 5 4 3 2 1 y 54 3 1 2 3 4 5 21 1 2 3 4 5 x f(x) 2x 3 5 4 3 2 1 y 5 4 31 2 1 2 3 45 1 2 3 4 5 x f(x) 3 Graphs of basic functions: The x-intercepts of a function are determined by finding the real solutions to the equation f 1x2 0. The y-intercept of a function is at f (0). Example 2 Find the x- and y-intercepts for the function pictured. f (x) (0, 1) (1, 0) (5, 0) 5 4 3 2 1 3 1 2 3 4 5 6 7 2 1 1 2 3 4 5 f1x2 0, when x 1 and x 5. The x-intercepts are (1, 0) and (5, 0). f102 The y-intercept is (0, 1). 1. x y f(x) f(x) x f(x) x f(x) x f(x) x2 f(x) x f(x) x3 f(x) x f(x) |x| f(x) x f(x) 1x f(x) x f(x) 1x
miller_intermediate_algebra_4e_ch1_3
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