QuestionQuestion 2 $0 / 1$ pt 5 9 Details
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 ). - $f(x)=3^{x}$ - $g(x)=$ $\square$ - $h(x)=$ $\square$

Studdy Solution

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 $g(x+1) = a \cdot 3^{x+1} = a \cdot 3 \cdot 3^x = 3 \cdot g(x)$ .

STEP 5

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:
$g(x) = 2 \cdot 3^x$
$h(x) = 5 \cdot 3^x$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms