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# which statement is true about the end behavior of the graphed function

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Which statement is true about the end behavior of the graphed function? O As the x-values go to positive infinity, the function's values go to negative infinity. O As the x-values go to zero, the function's values go to positive infinity. -4- O As the x-values go to negative infinity, the function's values are equal to zero. As the x-values go to positive infinity, the function's values go to positive infinity.

## Which statement is true about the end behavior of the graphed function? O As the x-values go to positive infinity, the function's values go to negative infinity. O As the x-values go to zero, the function's values go to positive infinity. -4- O As the x-values go to negative infinity, the function's values are equal to zero. As the x-values go to positive infinity, the function's values go to positive infinity.

Question Transcribed Image Text:Which statement is true about the end behavior of the graphed function? O As the x-values go to positive infinity, the function's values go to negative infinity. O As the x-values go to zero, the function's values go -2- to positive infinity. O As the x-values go to negative infinity, the function's values are equal to zero. 2. O As the x-values go to positive infinity, the function's values go to positive infinity. --4-

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## Which statement is true about the end behavior of the, graphed function? （ ）A. As the x

C | Snapsolve

Home/Class 10/Maths/

Question Maths Class 10

Which statement is true about the end behavior of the, graphed function? （ ） A. As the x

-values go to positive infinity, the function's values go to negative infinity.

B. As the x

-values go to zero, the function's values go to positive infinity.

C. As the x

-values go to negative infinity, the function's values are equal to zero.

D. As the x

-values go to positive infinity, the function's values go to positive infinity.

C

4.6

Correct 48 Incorrect 0

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## End behavior of polynomials (article)

Learn what the end behavior of a polynomial is, and how we can find it from the polynomial's equation. End behavior of polynomials

## End behavior of polynomials

Learn what the end behavior of a polynomial is, and how we can find it from the polynomial's equation.

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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 f f

describes the behavior of the graph of the function at the "ends" of the

x x x -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 x x -axis (as x x x approaches +\infty +∞ plus, infinity

) and to the left end of the

x x x -axis (as x x x approaches -\infty −∞ minus, infinity ). y y x x \blueD{y=f(x)} y=f(x)

\small{\gray{x \text{ gets}}}

x gets

\small{\gray{\text{more }+}}

more +

\small{\gray{f(x) \text{ gets}}}

f(x) gets

\small{\gray{\text{more }+}}

more +

For example, consider this graph of the polynomial function

f f f

. Notice that as you move to the right on the

x x x -axis, the graph of f f f

goes up. This means, as

x x x

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\rightarrow +\infty

x→+∞

x, right arrow, plus, infinity

,

f(x)\rightarrow +\infty

f(x)→+∞

f, left parenthesis, x, right parenthesis, right arrow, plus, infinity

. (Say, "as x x x

approaches positive infinity,

f(x) f(x)

f, left parenthesis, x, right parenthesis

approaches positive infinity.")

y y x x \blueD{y=f(x)} y=f(x)

\small{\gray{x \text{ gets}}}

x gets

\small{\gray{\text{more }-}}

more − \small{\gray{f(x)}} f(x)

\small{\gray{\text{gets}}}

gets

\small{\gray{\text{more}}}

more \small{\gray{-}} −

On the other end of the graph, as we move to the left along the

x x x -axis (imagine x x x approaching -\infty −∞ minus, infinity ), the graph of f f f

goes down. This means as

x x x

gets more and more negative,

f(x) f(x)

f, left parenthesis, x, right parenthesis

also gets more and more negative.

Mathematically, we write: as

x\rightarrow -\infty

x→−∞

x, right arrow, minus, infinity

,

f(x)\rightarrow -\infty

f(x)→−∞

f, left parenthesis, x, right parenthesis, right arrow, minus, infinity

. (Say, "as x x x

approaches negative infinity,

f(x) f(x)

f, left parenthesis, x, right parenthesis

approaches negative infinity.")

1) This is the graph of

y=g(x) y=g(x)

y, equals, g, left parenthesis, x, right parenthesis

What is the end behavior of

. y y x x g g g ? Choose 1 answer: Choose 1 answer: [I need help!]

## Determining end behavior algebraically

We can also determine the end behavior of a polynomial function from its equation. This is often helpful while trying to graph the function, as knowing the end behavior helps us visualize the graph at the "ends."

To determine the end behavior of a polynomial

f f f

from its equation, we can think about the function values for large positive and large negative values of

x x x .

Specifically, we answer the following two questions:

As

x\rightarrow +\infty

x→+∞

x, right arrow, plus, infinity

, what does f(x) f(x)

f, left parenthesis, x, right parenthesis

approach? As

x\rightarrow -\infty

x→−∞

x, right arrow, minus, infinity

, what does f(x) f(x)

f, left parenthesis, x, right parenthesis

approach?

### Investigation: End behavior of monomials

Monomial functions are polynomials of the form

y=ax^n y=ax n

y, equals, a, x, start superscript, n, end superscript

, where a a a

is a real number and

n n n

is a nonnegative integer.

Let's algebraically examine the end behavior of several monomials and see if we can draw some conclusions.

2) Consider the monomial

f(x)=x^2 f(x)=x 2

f, left parenthesis, x, right parenthesis, equals, x, squared

For very large positive

. x x x

values, what best describes

f(x) f(x)

f, left parenthesis, x, right parenthesis

For very large negative