Help with Algebraic Functions word problem.

Question

Karen bakes cookies. She has observed that the number of cookies that turn out well in each batch varies with the size of the batch and is given by the function f(x) = 2x – 23, where x is the size of the batch (number of cookies in each batch). She never bakes fewer than 12 cookies in a batch. If the size of five batches is {20, 25, 26, 27, 34}, how many cookies turn out well in each batch?

Answer 1

All you have to do is got through the sizes of each of the five batches, and use the number of cookies in the batch as x in the function.

 

For example, the first batch has a size of 20.  So go to the function definition -- f(x) = 2x – 23 -- and use 20 for x, and see what comes out:

 

f(x) = 2x – 23

f(20) = 2*20 - 23

f(20)) = 40 - 23 = 17

 

So 17 cookies turn out well in the first batch.

 

Go through each of the rest of the batches and do the same thing.

 

Remember, a function is like a machine.  You put something into it -- e.g., x or some value of x -- and the function definition tells you what to do with the input.  Just follow the instructions of the function, and something will come out.