1. Match the polynomial with its end behavior.
A. f(x) = -2x + 3
B. f(x) = x2 - 6x + 3
1. As x gets larger and larger in either
the positive or negative direction,
f(x) gets larger and larger in the
positive direction.
C. f(x) = 1 – x2 + 2x3
D.f(x) = 7 - x4
DE
2. As x gets larger and larger in the
positive direction, f(x) gets larger
and larger in the positive direction.
As x gets larger and larger in the
negative direction, f(x) gets larger
and larger in the negative direction.
3. As x gets larger and larger in the
positive direction, f(x) gets larger
and larger in the negative (help please)direction.
As x gets larger and larger in the
negative direction, f(x) gets larger
and larger in the positive direction.
4. As x gets larger and larger in either
the positive or negative direction,
f(x) gets larger and larger in the
negative direction.

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joaobezerra joaobezerra · Answer 1 · 2021-10-20T11:38:52+02:00

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:

[tex]f(x) = -2x + 3[/tex], then:

[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} -2x = -2(-\infty) = \infty[/tex]

[tex]\lim_{x \rightarrow \infty} f(x) \lim_{x \rightarrow -\infty} -2x = -2(\infty) = -\infty[/tex]

Thus, inverse directions, so matching pair with 3.

Function B:

[tex]f(x) = x^2 - 6x + 3[/tex], then:

[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} x^2 = (-\infty)^2 = \infty[/tex]

[tex]\lim_{x \rightarrow \infty} f(x) \lim_{x \rightarrow -\infty} x^2 = (\infty)^2 = \infty[/tex]

Always positive, so matching pair with 1.

Function C:

[tex]f(x) = 1 - x^2 + 2x^3[/tex], then:

[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 2x^3 = 2(-\infty)^3 = -\infty[/tex]

[tex]\lim_{x \rightarrow \infty} f(x) \lim_{x \rightarrow -\infty} 2x^3 = 2(\infty)^3 = \infty[/tex]

Same directions, thus, matching pair with 2.

Function D:

[tex]f(x) = 7 - x^4[/tex], then:

[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} -x^4 = -(-\infty)^4 = -\infty[/tex]

[tex]\lim_{x \rightarrow \infty} f(x) \lim_{x \rightarrow -\infty} -x^4 = -(\infty)^4 = -\infty[/tex]

Always negative, so matching pair with 4.

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