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.2

Given the information in the previous two questions and properties of both functions, choose which of the following statements is definitely true.

$f(x) > p(x)$ for $x >= 2524$ , since the steady percent increase of $f(x)$ means it will grow by ever greater amounts over a one unit interval. Although the amount that $p(x)$ increases over a one unit interval will also grow, it will do so more slowly.
$f(x) > p(x)$ may be true for all values of $x$ greater than or equal to 2524, or it may only be greater for some interval before $p(x)$ becomes greater. Since the percent increase of $p(x)$ is always changing, it cannot be certain which function will be greater.
$f(x) > p(x)$ for $2524 <= x < x_0$ , where $x_0$ is some real value of $x$ greater than 2524. Because $f(x)$ is only increasing by 1% each unit interval, the amount it increases over a one unit interval will eventually slow down, and $p(x)$ will become larger.
$f(x)$ will be equal to $p(x)$ for exactly one more value of x for $x > 2524$ . Let this point be $x_0$ . It cannot be determined with the information given which function will be greater for $x > x_0$ .

Question Info

Functions and Relations Question

Grade 11 Functions and Relations CCSS: HSF-LE.A.2