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).

Any function [tex]f(x) = \frac{bx}{a}[/tex], in which [tex]\frac{b}{a} = 3[/tex] is a tripling function, in which the value of f(x) is tripled whenever x changes by 1.

So

[tex]f(x) = \frac{9x}{3}[/tex]

[tex]f(x) = \frac{27x}{9}[/tex]

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MrRoyal MrRoyal · Answer 2 · 2021-10-26T13:50:58+02:00

Functions can be represented using equations.

The tripling functions are: [tex]\mathbf{g(x) = (log_3(27))^x}[/tex] and [tex]\mathbf{h(x) = (\frac{12}{4})^x}[/tex]

The function is given as:

[tex]\mathbf{f(x) = 3^x}[/tex]

To do this, we simply express 3 in another form

Using logarithms, we have:

[tex]\mathbf{3=log_3(27)}[/tex]

Substitute [tex]\mathbf{3=log_3(27)}[/tex] in [tex]\mathbf{f(x) = 3^x}[/tex]

So, we have:

[tex]\mathbf{g(x) = (log_3(27))^x}[/tex]

Also, we can express 3 as 12/4

So, we have:

[tex]\mathbf{h(x) = (\frac{12}{4})^x}[/tex]

Hence, the distinct tripling functions are:

[tex]\mathbf{g(x) = (log_3(27))^x}[/tex] and [tex]\mathbf{h(x) = (\frac{12}{4})^x}[/tex]