Question

Isaiah is standing in a stadium and has the option of running up a staircase or down astaircase for exercise. The function f(x) = 2 (17x] + 5x) will determine howmany calories Isaiah will burn if he runs up x steps. Use a negative value for x if heruns down the stairs. Find and interpret the given function values and determine anappropriate domain for the function.

Answer 1

f(x) = 1/25 ( l7xl + 5x )

f(-50) = 1/25 ( l 7 (-50) l + 5(-50) )

f(-50) = 1/25 ( l-350l -250 )

f(-50) = 1/25 (350-250)

f(-50) = 1/25 (100)

f(-50) = 4

-50 means down (negative) , he will burn 4 calories. the interpretation makes sense in the context of the problem.

f(20) = 1/25 ( l7 (20) l + 5*20)

f(20) = 1/25 ( 140+100)

f(20) = 9.6

means Isaiah runs up (positive) 20 stairs, he will burn 9.6 calories. It makes sense.

f(37.5) = 1/25 ( l 7 (37.5) l + 5*37.5 )

f(37.5 ) = 1/25 ( 262.5 + 187.5 )

f(37.5) = 18

he runs up (positive) , he will burn 18 calories, it does not make sense, because you can go up whole steps only ( no decimal)

Based on the observation, the domain ( possible x values ) is integers.