The function f ( x ) = 3 x is often referred to as the "tripling function" because f ( x ) triples whenever x changes by 1. give two more distinct examples of tripling functions (functions whose outputs triple whenever the input changes by 1).

Functions can be represented using equations.

The tripling functions are: and

The function is given as:

To do this, we simply express 3 in another form

Using logarithms, we have:

Substitute in

So, we have:

Also, we can express 3 as 12/4

So, we have:

Hence, the distinct tripling functions are:

and

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Step-by-step explanation:

Any function , in which is a tripling function, in which the value of f(x) is tripled whenever x changes by 1.

So

55 lbs of $0.40 and 45 lbs of $1.40  

Step-by-step explanation:

Let's say that we have two buckets, one that weighs x pounds and the candies in it are $0.40 per pound and another that weighs 100-x pounds (because we know the two added together must be 100 pounds) and the candies in it are $1.40 per pound.

There is a third bucket that is made when you combine the two, it weighs 100 pounds and the candies in it are $0.85. Multiply the cents per pound by the pounds of the candy for each bucket and you get this equation:

0.4 * x + 1.4 (100-x) = 0.85 * 100

Solve!

0.4x + 140 - 1.4x = 85

-x + 140 = 85

-x = -55

x = 55

From this we get that 100 - x = 45.

So, the answer is 55 lbs of $0.40 and 45 lbs of $1.40