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Stewart Calculus ET 5e 0534393217;1. Functions and Models; 1.1 Four Ways to Represent a Function

1. (a) The point ( 1, 2 ) is on the graph of f , so f ( 1)= 2 . (b) When x=2 , y is about 2.8 , so f (2) 2.8 . (c) f (x)=2 is equivalent to y=2 . When y=2 , we have x= 3 and x=1 . (d) Reasonable estimates for x when y=0 are x= 2.5 and x=0.3 . (e) The domain of f consists of all x values on thegraph of f . For this function, the domain is 3 x 3 , or 3,3 . The range of f consists of all y values on the graph of f . For this function, the range is 2 y 3 , or 2,3 . (f) As x increases from 1 to 3 , y increases from 2 to 3 . Thus, f is increasing on the interval 1,3 . 2. (a) The point ( 4, 2 ) is on the graph of f , so f ( 4)= 2 . The point ( 3,4 ) is on the graph of g , so g(3)=4 . (b) We arelooking for the values of x for which the y values are equal. The y values for f and g are equal at the points ( 2,1 ) and ( 2,2 ) , so the desired values of x are 2 and 2 . (c) f (x)= 1 is equivalent to y= 1 . When y= 1 , we have x= 3 and x=4 . (d) As x increases from 0 to 4 , y decreases from 3 to 1 . Thus, f is decreasing on the interval 0,4 . (e) The domain of f consists of all x values on thegraph of f . For this function, the domain is 4 x 4 , or 4,4 . The range of f consists of all y values on the graph of f . For this function, the range is 2 y 3 , or 2,3 . (f) The domain of g is 4,3 and the range is 0.5,4 . 3. From Figure 1 in the text, the lowest point occurs at about ( t,a ) = ( 12, 85) . The highest point occurs at about ( 17,115) . Thus, the range of the vertical groundacceleration is 85 a 115 . In Figure 11, the range of the north south acceleration is approximately 325 a 485 . In Figure 12, the range of the east west acceleration is approximately 210 a 200 . 4. Example 1: A car is driven at 60 mi / h for 2 hours. The distance d traveled by the car is a function of the time t . The domain of the function is {t |0 t 2} , where t is measured in hours. The range of thefunction is { d |0 d 120} , where d is measured in miles.

Example 2: At a certain university, the number of students N on campus at any time on a particular day is a function of the time t after midnight. The domain of the function is {t |0 t 24} , where t is measured in hours. The range of the function is { N |0 N k} , where N is an integer and k is the largest number of students on campus atonce.

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Stewart Calculus ET 5e 0534393217;1. Functions and Models; 1.1 Four Ways to Represent a Function

Example 3: A certain employee is paid $8.00 per hour and works a maximum of 30 hours per week. The number of hours worked is rounded down to the nearest quarter of an hour. This employee’s gross weekly pay P is a function of the number of hours worked h . The domain of the function is0,30 and the range of the function is { 0,2.00,4.00,... ,238.00,240.00} .

5. No, the curve is not the graph of a function because a vertical line intersects the curve more than once. Hence, the curve fails the Vertical Line Test. 6. Yes, the curve is the graph of a function because it passes the Vertical Line Test. The domain is [ 2,2] and the range is [ 1,2] . 7. Yes, the curve is the graphof a function because it passes the Vertical Line Test. The domain is [ 3,2] and the range is 3, 2 ) [ 1,3] . 8. No, the curve is not the graph of a function since for x=0 , points on the curve. 1 , and 2 , there are infinitely many

9. The person’s weight increased to about 160 pounds at age 20 and stayed fairly steady for 10 years. The person’s weight dropped to about 120 pounds for the next 5years, then increased rapidly to about 170 pounds. The next 30 years saw a gradual increase to 190 pounds. Possible reasons for the drop in weight at 30 years of age: diet, exercise, health problems. 10. The salesman travels away from home from 8 to 9 A.M. and is then stationary until 10 : 00 . The salesman travels farther away from 10 until noon. There is no change in his distance from home...