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.

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 =  ,

∴ the number of gallons of LF by mixing x tsp of powder fertiliser =

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,

is a function,

Now, by graphing,

It is clear that the equation follow the vertical line test,

That is, it is a function.

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