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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.

1 Match the polynomial with its end behavior A fx 2x 3 B fx x2 6x 3 1 As x gets larger and larger in either the positive or negative direction fx gets larger an class=

Respuesta :

Using infinity limits, the matching pairs are:

  • A - 3.
  • B - 1.
  • C - 2.
  • D - 4.

The end behavior of a function f(x) is given by:

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

Function A:

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

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

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

Thus, matches with item 3.

Function B:

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

[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} x^2 - 6x + 3 = \lim_{x \rightarrow -\infty} x^2 = (-\infty)^2 = \infty[/tex]

[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} x^2 - 6x + 3 = \lim_{x \rightarrow \infty} x^2 = (\infty)^2 = \infty[/tex]

Thus, matches with item 1.

Function C:

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

[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 1 - x^2 + 2x^3 = \lim_{x \rightarrow -\infty} 2x^3 = 2(-\infty)^3 = -\infty[/tex]

[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 1 - x^2 + 2x^3 = \lim_{x \rightarrow \infty} 2x^3 = 2(\infty)^3 = \infty[/tex]

Thus, matches with item 2.

Function D:

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

[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 7 - x^4 = \lim_{x \rightarrow -\infty} -x^4 = -(-\infty)^4 = -\infty[/tex]

[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 7 - x^4 = \lim_{x \rightarrow \infty} -x^4 = -(\infty)^4 = -\infty[/tex]

Thus, matches with item 4.

A similar problem is given at https://brainly.com/question/24248193

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