Question

The function

f
(
x
)
=
3
x
is often referred to as a tripling function because
f
(
x
)
triples whenever
x
changes by
1
. But this is not the only example of a tripling function. Give two more distinct examples of tripling functions (functions whose values triple whenever the independent variable changes by
1
).

f
(
x
)
=
3
x
g
(
x
)
=

syntax error

Warning:
g
is not a tripling function.

h
(
x
)
=

syntax error

Warning:
h
is not a tripling function.

Answer 1

There are indeed several examples of tripling functions, where the function's values triple whenever the independent variable changes by 1. Here are two distinct examples:

1. Function: f(x) = 2x

Explanation: In this case, for every unit increase in x, the value of f(x) triples. Let's consider a few values to illustrate this:

- f(0) = 2(0) = 0

- f(1) = 2(1) = 2

- f(2) = 2(2) = 4

- f(3) = 2(3) = 6

As we can see, when x increases by 1, the value of f(x) triples. For example, when x changes from 1 to 2, f(x) changes from 2 to 4, tripling its initial value.

2. Function: g(x) = -5x

Explanation: In this case, the function g(x) also exhibits tripling behavior. Let's examine a few values:

- g(0) = -5(0) = 0

- g(1) = -5(1) = -5

- g(2) = -5(2) = -10

- g(3) = -5(3) = -15

Similar to the previous example, when x increases by 1, the value of g(x) triples in magnitude but with a negative sign. For instance, when x changes from 1 to 2, g(x) changes from -5 to -10, tripling its initial value.

It is important to note that these examples are not exhaustive, and there are numerous other functions that exhibit tripling behavior. The key characteristic is that the function's values triple whenever the independent variable changes by 1.

Explanation: