Find f (2) for each function. a) f {(5, 8), (1, 2), (2, 3), (6, 9)} b) Domain f Range c) x y 5 2 3 7 5 2 0 y f x 5 5 Evaluate a Function for Variables or Expressions Functions can be evaluated for variables or expressions. EXAMPLE 8 Let h(x) 5x 3. Find each of the following and simplify. a) h(c) b) h(t 4) Solution a) Finding h(c) (read as h of c) means to substitute c for x in the function h, and simplify the expression as much as possible. h(x) 5x 3 h(c) 5c 3 Substitute c for x. b) Finding h(t 4) (read as h of t minus 4) means to substitute t 4 for x in function h, and simplify the expression as much as possible. Since t 4 contains two terms, we must put it in parentheses. h(x) 5x 3 h(t 4) 5(t 4) 3 Substitute t 4 for x. h(t 4) 5t 20 3 Distribute. h(t 4) 5t 17 Combine like terms. Let f (x) 2x 7. Find each of the following and simplify. a) f (k) b) f (p 3) 6 Define and Graph a Linear Function Earlier in this chapter, we learned that a linear equation can have the form y mx b. Similarly, a linear function has the form f (x) mx b. YOU TRY 7 Notice that h(c) indicates that we replace the x-value with c. Notice that h(t 4) indicates that we replace the x-value with t 4. YOU TRY 8 Remember that a vertical line has a undefined slope. Its equation cannot be written in y mx b form. The graph of a vertical line does not represent a function. Definition A linear function has the form f (x) mx b, where m and b are real numbers, m is the slope of the line, and (0, b) is the y-intercept. 206 CHAPTER 4 Linear Equations in Two Variables and Functions www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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