Math Snap

STEP 1

1. A tripling function is defined as a function whose value triples when the independent variable increases by 1.
2. The function $f(x) = 3^x$ is given as an example of a tripling function.
3. We need to find two more distinct functions that also triple when the independent variable increases by 1.

STEP 2

1. Understand the properties of a tripling function.
2. Identify the mathematical form of a tripling function.
3. Construct two distinct examples of tripling functions.

STEP 3

A tripling function is characterized by the property that for any $x$, the function value at $x+1$ is three times the function value at $x$.
This means if $g(x)$ is a tripling function, then $g(x+1) = 3 \cdot g(x)$.

STEP 4

The mathematical form of a tripling function can be generalized as $g(x) = a \cdot 3^x$, where $a$ is a constant.
This form satisfies the condition $g(x+1) = a \cdot 3^{x+1} = a \cdot 3 \cdot 3^x = 3 \cdot g(x)$.

To create two distinct examples, choose different values for the constant $a$.
Example 1: Let $a = 2$. Then $g(x) = 2 \cdot 3^x$.
Example 2: Let $a = 5$. Then $h(x) = 5 \cdot 3^x$.
Both functions $g(x) = 2 \cdot 3^x$ and $h(x) = 5 \cdot 3^x$ are tripling functions.
The two distinct examples of tripling functions are:
$$g(x) = 2 \cdot 3^x$$ $$h(x) = 5 \cdot 3^x$$