SECTION 2.2 The Graph of a Function 81 (c) The energy expended for a walking speed of v 100 = meters per minute is E 100 29 100 0.0053 100 0.82 cal min kg ( ) = + ⋅ = (d) See Figure 20 for the graph of E E v( ) = on a TI-84 Plus CE. (e) With the function E E v( ) = in Y ,1 we create Table 3. Scroll down to find a value of v for which Y1 is smallest.Table 4 shows that a walking speed of v 74 = meters per minute minimizes the expended energy at about 0.784 cal min kg. Figure 20 E v v v 29 0.0053 ( ) = + 1.5 0 200 Table 3 Table 4 Now Work PROBLEM 35 SUMMARY • Graph of a Function The set of points x y , ( ) in the xy -plane that satisfy the equation y f x . ( ) = • Vertical-Line Test A set of points in the xy -plane is the graph of a function if and only if every vertical line intersects the graph in at most one point. ‘Are You Prepared?’ Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red. 2.2 Assess Your Understanding 1. The intercepts of the equation x y4 16 2 2 + = are . (pp. 20–21) 2. True or False The point 2, 6 ( ) − − is on the graph of the equation x y2 2. = − (pp. 4–8) Concepts and Vocabulary 3. A set of points in the xy -plane is the graph of a function if and only if every line intersects the graph in at most one point. 4. If the point 5, 3 ( ) − is a point on the graph of f, then f . ( ) = 5. Find a so that the point 1, 2 ( ) − is on the graph of f x ax 4. 2 ( ) = + 6. True or False Every graph represents a function. 7. True or False The graph of a function y f x( ) = always crosses the y -axis. 8. True or False The y -intercept of the graph of the function y f x , ( ) = whose domain is all real numbers, is f 0 . ( ) 9. Multiple Choice If a function is defined by an equation in x and y, then the set of points x y , ( ) in the xy -plane that satisfy the equation is called the . (a) domain of the function (b) range of the function (c) graph of the function (d) relation of the function 10. Multiple Choice The graph of a function y f x( ) = can have more than one of which type of intercept? (a) x -intercept (b) y -intercept (c) both (d) neither 1. Now Work 1. Modeling 1.ExplainingConcepts Calculus Preview 1.InteractiveFigure
RkJQdWJsaXNoZXIy NjM5ODQ=