Question

You can make 5 gal of liquid fertilizer by mixing 8 tsp of powdered fertilizer with water: Represent the relationship between the tablespoons of powder used and the gallons of fertilizer made using a table, an equation, and a graph. Is the amount of fertilizer made a function of the amount of powder used? Explain.

Answer 1

do u want the graph also with the answer???

Answer 2

Let y represents the number of gallons of fertilisers obtained by mixing x tsp of powder fertiliser

Given,

The number of gallons of liquid fertiliser by mixing 8 tsp of powder fertiliser = 5,

So, the number of gallons of liquid fertiliser by mixing 1 tsp of powder fertiliser =
`(5)/(8)`,

∴ the number of gallons of LF by mixing x tsp of powder fertiliser =
`(5)/(8)x`

`\implies y =(5)/(8)x`

Which is the required equation.

Since, in the equation, for every distinct value of x there are distinct value of y,

Thus, the above relation is a function.

By the table,

x 1 2 3 4 5

y 5/8 5/4 15/8 5/2 25/8

It is clear that for each input value there are distinct output value,

`y=(5)/(8)x` is a function,

Now, by graphing,

It is clear that the equation
`y=(5)/(8)x` follow the vertical line test,

That is, it is a function.