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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

The following are some more values of

$f(x)$ and

$p(x)$ , which have been rounded. Which of the following statements are supported by this information, and general properties of these functions? Choose all correct answers.

$\ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ \ \ \ \ \mathbf{p(x)} \ \ \ \ \ \ \ \ \ \$
$2521$	$7.8376 xx 10^10$	$8.0110 xx 10^10$
$2522$	$7.9160 xx 10^10$	$8.0206 xx 10^10$
$2523$	$7.9951 xx 10^10$	$8.0301 xx 10^10$
$2524$	$8.0751 xx 10^10$	$8.0397 xx 10^10$
$2525$	$8.1558 xx 10^10$	$8.0492 xx 10^10$

$f(x) < p(x)$ for $x <= 2523$ .
The percent increase of $f(x)$ over a one unit interval continues to be about 1%.
The percent increase of $p(x)$ over a one unit interval continues to decrease.
The average rate of change of $p(x)$ over a one unit interval is greater than that of $f(x)$ for these values of $x$ .