Respuesta :
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 [tex] k \in \mathbb{R} [/tex] such that your function is in the form
[tex] f(x) = kx [/tex]
In fact, if you double the input, you have
[tex] f(2x) = k\cdot(2x) = 2\cdot (kx) = 2f(x) [/tex]
And similarly
[tex] f(3x) = k\cdot(3x) = 3\cdot (kx) = 3f(x) [/tex]
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 [tex] y=kx[/tex].
For example, the function
[tex] f(x) = \dfrac{x^3}{3} - 2x^2 + \dfrac{14}{3}x -2 [/tex]
is such that
[tex] f(1) = 1,\ f(2) = 2,\ f(3) = 3 [/tex]
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,
[tex] f(2) = 2,\ f(4) = 6 [/tex]
And so doubling the input didn't double the output.
Answer:
The function is most likely directly proportional.
More input results in more output.
Step-by-step explanation:
Apex
