Question

if you double the input of a function and it results in twice the output and if you triple the input and it result in three times the output what can be guessed about the function.

Answer 1

A function behaving as you state is a linear function, which means that the output varies directly with the input.

So, there exists some constant $k \in \mathbb{R}$ such that your function is in the form

$f(x) = kx$

In fact, if you double the input, you have

$f(2x) = k\cdot(2x) = 2\cdot (kx) = 2f(x)$

And similarly

$f(3x) = k\cdot(3x) = 3\cdot (kx) = 3f(x)$

Note that this is a guess, it may happen that output doubles (triples) if you double (triple) the input, and still the function is not like $y=kx$.

For example, the function

$f(x) = \dfrac{x^3}{3} - 2x^2 + \dfrac{14}{3}x -2$

is such that

$f(1) = 1,\ f(2) = 2,\ f(3) = 3$

So, it may seems that doubling and tripling the input doubles and triples the output, but this is not true for every input, for example,

$f(2) = 2,\ f(4) = 6$

And so doubling the input didn't double the output.

Answer 2

Answer:

The function is most likely directly proportional.

More input results in more output.

Step-by-step explanation:

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