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Type: Multiple-Choice
Category: Functions and Relations
Level: Grade 11
Standards: HSF-LE.A.3
Author: nsharp1
Last Modified: 4 years ago

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Functions and Relations Question

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Let

$f(x)$ be an exponential function and

$p(x)$ a 3rd degree polynomial function. Assume that

$p(x)$ has 3 real zeros, which are all less than or equal to zero.

Grade 11 Functions and Relations CCSS: HSF-LE.A.3

Below is a table of some of the values of

$f(x)$ and

$p(x)$ , rounded to 4 decimal places if necessary. What conclusions can be seen from this information? Choose all correct answers.

$\ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ \ \ \ \ \mathbf{p(x)} \ \ \ \ \ \ \ \ \ \$
$1$	$1.01$	$5$
$2$	$1.0201$	$40$
$3$	$1.0303$	$135$
$4$	$1.0406$	$320$
$5$	$1.0510$	$625$

That $p(x) > f(x)$ for all values of $x>1$ .
That, for these values, the average rate of change over a one unit interval of $p(x)$ is greater than that of $f(x)$ .
That $f(x)$ has a percent increase of about 1%.
That the percent increase of $p(x)$ over a one unit interval is declining.