Polynomial Functions and End Behavior
AP Precalculus · Flashcards
AP PRECALCULUS · FLASHCARDS
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QUESTION
State the polynomial type for
f
(
x
)
=
x
3
−
4
x
+
2
f(x) = x^3 - 4x + 2
f
(
x
)
=
x
3
−
4
x
+
2
.
QUESTION
What is the end behavior of
f
(
x
)
=
x
7
−
x
5
+
x
f(x) = x^7 - x^5 + x
f
(
x
)
=
x
7
−
x
5
+
x
as
x
→
infinity
x \to \text{infinity}
x
→
infinity
?
QUESTION
What is the end behavior of
f
(
x
)
=
−
4
x
3
+
2
x
−
5
f(x) = -4x^3 + 2x - 5
f
(
x
)
=
−
4
x
3
+
2
x
−
5
as
x
→
−
infinity
x \to -\text{infinity}
x
→
−
infinity
?
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ANSWER
f
(
x
)
→
infinity
f(x) \to \text{infinity}
f
(
x
)
→
infinity
. Odd degree with negative leading coefficient:
x
→
−
∞
x \to -\infty
x
→
−
∞
gives
f
(
x
)
→
+
∞
f(x) \to +\infty
f
(
x
)
→
+
∞
.
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