Question

The inverse variation xy = 20 relates the speed x in miles per hour to the time y in hours for a person to travel 20 miles. Determine a reasonable domain and range, and then graph the inverse variation. Use the graph to estimate the speed needed in order to travel 20 miles in 8 hours.A. domain: x > 0; range: y > 0You need a speed of about 0.5 miles per hour to travel 20 miles in 8 hoursB.domain: x ≥ 0; range: y > 0You need a speed of about 2 miles per hour to travel 20 miles in 8 hoursc.domain: x > 0; range: y > 0You need a speed of about 4 miles per hour to travel 20 miles in 8 hoursd.domain: x > 0; range: y > 0You need a speed of about 2.5 miles per hour to travel 20 miles in 8 hours

Answer 1

we have the equation

xy=20

where

y ----> is the time in hours

x ----> is the speed in miles per hours

so

y=20/x

using a graphing tool

The domain ---> Remember that the denominator cannot be equal to zero

so

x>0

The range

The graph has a vertical asymptote at x=0 and a horizontal asymptote at y=0

so

The range is the interval (0, infinite)

therefore

The answer is the option d

domain: x > 0; range: y > 0

You need a speed of about 2.5 miles per hour to travel 20 miles in 8 hours