Section 2.6 Introduction to Functions 197 4. Finding Function Values from a Graph We can find function values by looking at a graph of the function.The value of f(a) refers to the y-coordinate of a point with x-coordinate a. Finding Function Values from a Graph Example 5 Consider the function pictured in Figure 2-34. a. Find h112 . b. Find h122 . c. Find h152 . d. For what value of x is h1x2 3? e. For what values of x is h1x2 0? Solution: a. h112 2 This corresponds to the ordered pair (1, 2). b. h122 1 This corresponds to the ordered pair (2, 1). c. h152 is not defined . The value 5 is not in the domain. d. h1x2 3 for x 4 This corresponds to the ordered h1x2 x 3 x 4 0 h(x) 5 y h(x) 4 3 2 1 54 321 1 2 3 4 5 1 2 3 4 5 Figure 2-34 pair (4, 3). e. for and These are the ordered pairs (3, 0) and (4, 0). Skill Practice Refer to the function graphed here. 13. Find f (0). 14. Find f (2). 15. Find f (5). 16. For what value(s) of x is f (x) 0? 17. For what value(s) of x is f (x) 4? x 5 y 4 3 2 1 y f(x) 54 321 1 2 3 4 5 1 2 3 4 5 x 5. Domain of a Function A function is a relation, and it is often necessary to Consider a function defined by the equation y f 1x2 determine its domain and range. .The domain of f is the set of all x-values that when substituted into the function produce a real number.The range of f is the set of all y-values corresponding to the values of x in the domain. y f 1x2, To find the domain of a function defined by keep these guidelines in mind. • 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. Answers 13. 3 14. 1 15. Not defined 16. 17. x 5 x 4 and x 4
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