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Problem-Solving and Data Analysis / Two-variable data: Models and scatterplots Difficulty: Hard

For $x greater than 0$ , the function $f$ is defined as follows:

$f (x)$ equals $201 percent sign$ of $x$

Which of the following could describe this function?

Decreasing exponential

Decreasing linear

Increasing exponential

Increasing linear

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Explanation

Choice D is correct. It's given that for $x greater than 0$ , $f (x)$ is equal to $201 percent sign$ of $x$ . This is equivalent to $f (x) = \frac{201}{100} x$ , or $f left parenthesis x right parenthesis equals 2.01 x$ , for $x greater than 0$ . This function indicates that as $x$ increases, $f (x)$ also increases, which means $f$ is an increasing function. Furthermore, $f (x)$ increases at a constant rate of $2.01$ for each increase of $x$ by $1$ . A function with a constant rate of change is linear. Thus, the function $f$ can be described as an increasing linear function.

Choice A is incorrect and may result from conceptual errors.

Choice B is incorrect and may result from conceptual errors.

Choice C is incorrect. This could describe the function $f left parenthesis x right parenthesis equals left parenthesis 2.01 right parenthesis Superscript x$ , where $f (x)$ is equal to $201 percent sign$ of $f left parenthesis x minus 1 right parenthesis$ , not $x$ , for $x greater than 0$ .