Answer:
Step-by-step explanation:
In this lesson, you will learn what the "end behavior" of a polynomial is and how to analyze it from a graph or from a polynomial equation.
What's "end behavior"?
The end behavior of a function
f
ff describes the behavior of the graph of the function at the "ends" of the
x
xx-axis.
In other words, the end behavior of a function describes the trend of the graph if we look to the right end of the
x
xx-axis (as
x
xx approaches
+
∞
+∞plus, infinity) and to the left end of the
x
xx-axis (as
x
xx approaches
−
∞
−∞minus, infinity).
yyxxy=
f(x)
y=f(x)
x gets
x gets
more
+ more +
f(x) gets
f(x) gets
more
+ more +
For example, consider this graph of the polynomial function
fff. Notice that as you move to the right on the x
xx-axis, the graph of f
ff goes up. This means, as x
xx gets larger and larger,
f(x)
f(x)f, left parenthesis, x, right parenthesis gets larger and larger as well. Mathematically, we write: as
x→+x→+∞x, right arrow, plus, infinity,
f(x)→+∞
f(x)→+∞f, left parenthesis, x, right parenthesis, right arrow, plus, infinity. (Say, "as xxx approaches positive infinity, f(x)
f(x)f, left parenthesis, x, right parenthesis approaches p
