Question Info

This question is public and is used in 1 group and 6 tests or worksheets.

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

View all questions by nsharp1.

Functions and Relations Question

View Find Similar

View this question.

Add this question to a group or test by clicking the appropriate button below.

Note: This question is included in a group. The contents of the question may require the group's common instructions or reference text to be meaningful. If so, you may want to add the entire group of questions to your test. To do this, click on the group instructions in the blue box below. If you choose to add only this question, common instructions or reference text will not be added to your test.

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

For a general exponential function

$g(x) = cb^x, c>0, b>0 " and " b!=1$ and a general polynomial function

$P(x) = a_1 x^n + a_2 x^{n-1} + ... + a_n x + a_{n+1}, \ \ a_1 > 0$ , which of the following conclusions is correct?

Without knowing more about the specific functions, no conclusion can be made.
That for an even degree polynomial, $P(x) > g(x)$ , but for an odd degree polynomial $g(x) > P(x)$ .
That, as long as $P(x)$ has no maximum or minimums for $x>0$ , $P(x) > g(x)$ . Otherwise, $g(x) > P(x)$ .
That there will always exist a value $x_0$ such that $g(x) > P(x)$ for $x > x_0$ .