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

$x$ $x$	$f (x)$ $f (x)$
$- 1$ $negative 1$	$16$ $16$
$0$ $0$	$17$ $17$
$1$ $1$	$18$
$2$	$19$

The table shows selected values from function $f$ .

Which of the following is the best description of function $f$ ?

Decreasing linear

Increasing linear

Decreasing exponential

Increasing exponential

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Explanation

Choice B is correct. The given values show that as $x$ increases, $f (x)$ also increases, which means that $f$ is an increasing function. Furthermore, $f (x)$ increases at a constant rate of $1$ 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. For a decreasing linear function, as $x$ increases, $f (x)$ decreases rather than increases.

Choice C is incorrect. For a decreasing exponential function, for each increase of $x$ by $1$ , $f (x)$ decreases by a fixed percentage rather than increases at a constant rate.

Choice D is incorrect. For an increasing exponential function, for each increase of $x$ by $1$ , $f (x)$ increases by a fixed percentage rather than at a constant rate.