How do you find the end behavior?

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

,kjhgfd

step-by-step explanation: