Evaluate And Graph Polynomial Functions Page 2
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1
2
3
4The second method is called synthetic substitution. It is easier to demonstrate than to explain in
words, so we’ll look at the example from (a) but with the new method.
( )
= 2x
− 5x
− 4x + 8
4
3
Example: Evaluate
when x = 3 using synthetic substitution.
f x
Now try a couple yourself.
3. Evaluate using synthetic substitution.
f (x) = x
+ 7x
− 8x
− 14x + 8
(a)
when x = –2
4
3
2
1
x =
g(x) = −x
+ 5x
+ 3x − 2
(b)
5
3
when
[Don’t forget the place-holders!]
2
∞
−∞
The end behavior of a function refers to its behavior as x approaches
or
.
y = −x
For example, the figure below shows the graph of
3
. Do you see why its end behavior is
written this way?
End behavior:
∞ f (x)
−∞
As x approaches
,
approaches
.
−∞ f (x)
∞
As x approaches
,
approaches
.
As x → ±∞, y → ∞ .
This can also be written in more compactly form:
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