Question

Write three functions. In the first function, y should vary directly with x. In the second function, y should vary inversely with x. In the third function, the relationship between x and y should be neither inverse variation nor direct variation. Describe the graph of each function and give a real-world example for each.

Answer 1

   we have

1) y should vary directly with x

y = kx ------ > that means that when x increases, y increases or vice versa by the same factor k

Example--- >  A car runs x hour with speed 5 m/h --> Distance y =  5x

2) y should vary inversely with x

y = k/x ------ > that means that when x  increases, y decreases or vice versa by the same factor k

Example------- > A distance of 360km can be covered 

in 3 hours at a speed of 120kph
in 4 hours at a speed of 90kph

Y=360/x------ > y is the speed of a car at time x and 360 is the proportionality constant

3) the relationship between x and y should be neither inverse variation nor direct variation

y = 1.8x +32

Temperatures in degrees Fahrenheit are linearly related to those in degrees Celsius, but the relation is neither directly nor inversely proportional.

see the attached figure to see the graph