Question

1. Match the polynomial with its end behavior.

Answer 1

Using limit concepts, the matching pairs are:

A - 3

B - 1

C - 2

D - 4

The end behavior of a function f(x) is given by it's limit as x goes to infinity.

Function A:

$f(x) = -2x + 3$, then:

$\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} -2x = -2(-\infty) = \infty$

$\lim_{x \rightarrow \infty} f(x) \lim_{x \rightarrow -\infty} -2x = -2(\infty) = -\infty$

Thus, inverse directions, so matching pair with 3.

Function B:

$f(x) = x^2 - 6x + 3$, then:

$\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} x^2 = (-\infty)^2 = \infty$

$\lim_{x \rightarrow \infty} f(x) \lim_{x \rightarrow -\infty} x^2 = (\infty)^2 = \infty$

Always positive, so matching pair with 1.

Function C:

$f(x) = 1 - x^2 + 2x^3$, then:

$\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 2x^3 = 2(-\infty)^3 = -\infty$

$\lim_{x \rightarrow \infty} f(x) \lim_{x \rightarrow -\infty} 2x^3 = 2(\infty)^3 = \infty$

Same directions, thus, matching pair with 2.

Function D:

$f(x) = 7 - x^4$, then:

$\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} -x^4 = -(-\infty)^4 = -\infty$

$\lim_{x \rightarrow \infty} f(x) \lim_{x \rightarrow -\infty} -x^4 = -(\infty)^4 = -\infty$

Always negative, so matching pair with 4.

A similar problem is given at brainly.com/question/9368215