31. Open-Ended Write an equation for a horizontal translation of y = 2 x . y equals , 2 over x , .  Then write an equation for a vertical translation of y = 2 x . y equals , 2 over x , .  Identify the horizontal and vertical asymptotes of the graph of each function.

Sketch the graph of each function.

32. xy = 3
33. xy + 5 = 0
34. 3xy = 1
35. 5xy = 2
36. 10 x y = − 4 10 x y equals negative 4

37. Writing Explain how knowing the asymptotes of a translation of y = 1 x y equals , 1 over x  can help you graph the function. Include an example.

38. Multiple Choice The formula p = 69.1 a + 2.3 p equals . fraction 69.1 , over eh plus 2.3 end fraction  models the relationship between atmospheric pressure p in inches of mercury and altitude a in miles.

    Use the data shown with the photo. At which location does the model predict the pressure to be about 23.93 in. of mercury? (Hint: 1 mi = 5280 ft.)

    1. Sahara Desert
    2. Kalahari Desert
    3. Mt. Kilimanjaro
    4. Vinson Massif

    

Graphing Calculator Graph each pair of functions. Find the approximate point(s) of intersection.

39. y = 6 x − 2 , y = 6 y equals . fraction 6 , over x minus 2 end fraction . comma y equals 6
40. y = − 1 x − 3 − 6 , y = 6.2 y equals negative . fraction 1 , over x minus 3 end fraction . minus 6 comma y equals 6.2
41. y = 3 x + 1 , y = − 4 y equals . fraction 3 , over x plus 1 end fraction . comma y equals negative 4
42. Reasoning How will the domain and the range of the parent function y = 1 x y equals , 1 over x  change after the translation of its graph by 3 units up and by 5 units to the left?
43. 1. Gasoline Mileage Suppose you drive an average of 10,000 miles each year. Your gasoline mileage (mi/gal) varies inversely with the number of gallons of gasoline you use each year. Write and graph a model for your average mileage m in terms of the gallons g of gasoline used.
    2. After you begin driving on the highway more often, you use 50 gal less per year. Write and graph a new model to include this information.
    3. Calculate your old and new mileage assuming that you originally used 400 gal of gasoline per year.

C Challenge

Reasoning Compare each pair of graphs and find any points of intersection.

44. y = 1 x  and  y = | 1 x | y equals , 1 over x , and , y equals absolute value of , 1 over x , end absolute value ,
45. y = 1 x  and  y = 1 x 2 y equals , 1 over x , and , y equals , fraction 1 , over x squared end fraction
46. y = | 1 x |  and  y = 1 x 2 y equals absolute value of , 1 over x , end absolute value , . and , y equals , fraction 1 , over x squared end fraction
47. Find two reciprocal functions such that the minimum distance from the origin to the graph of each function is 4 2 . 4 , square root of 2 . end root
48. Write each equation in the form y = k x − b + c , y equals . fraction k , over x minus b end fraction . plus c comma  and sketch the graph.
    1. y = 2 3 x − 6 y equals . fraction 2 , over 3 x minus 6 end fraction
    2. y = 1 2 − 4 x y equals . fraction 1 , over 2 minus 4 x end fraction
    3. y = 3 − x x + 2 y equals . fraction 3 minus x , over x plus 2 end fraction
    4. x y − y = 1 x y minus y equals 1

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