End Behavior

Key Questions

What does a function's end behavior mean?

Answer:

The end behavior of a function is the behavior of the graph of the function $f(x)$ as $x$ approaches positive infinity or negative infinity.

Explanation:

The end behavior of a function is the behavior of the graph of the function $f(x)$ as $x$ approaches positive infinity or negative infinity.

This is determined by the degree and the leading coefficient of a polynomial function.

For example in case of $y=f(x)=1/x$ , as $x->+-oo$ , $f(x)->0$ .
graph{1/x [-10, 10, -5, 5]}
But if $y=f(x)=(3x^2+5)/((x+2)(x+7))$ as $x->+-oo$ , $y->3$
graph{(3x^2+5)/((x+2)(x+7)) [-165.7, 154.3, -6, 12]}

Shwetank Mauria · 1 · Feb 26 2017

Questions

What does a function's end behavior mean?
How do you describe the end behavior of a cubic function?
How do you find the end behavior of a quadratic function?
What is the end behavior of $f(x) = 3x^4 - x^3 + 2x^2 + 4x + 5$ ?
What is the end behavior of $f(x) = (x - 2)^4(x + 1)^3$ ?
What is the end behavior of the graph $f(x)=x^5-2x^2+3$ ?
What is the degree of the Polynomial $3-4z^4 w^8u^6 7u^9zw^8$ ?
How do you find the degree of the polynomial $12-10x$ ?
What is the degree of the polynomial $–4x^3 + 2x^2y – 5xy^4$ ?
What is the degree of the polynomial $8x^2$ ?
What is the degree and leading coefficient of this polynomial $4y+18y^2+8-10y^4$ ?
How do you find the degree of $-(x-4)(+1)^2(x-1)^3$ ?
What is the name of a polynomial of degree 3?
How do you determine the degree, terms and coefficients or the following polynomial $3x^7$ ?
How do you find the degree of a polynomial in two variables?
What is the degree of the polynomial $5x^5 + 8x^2 + 2x - 3x^9 - 8x^4 - 4x^5$ ?
What is the degree of $9xy^3z^6$ ? (second problem) $3x^3 - 2x^2y^2 + y^2$ ?
What is the degree of $P(x) = x^3(x+2)(x-3)^2$ ?
How do you find the degree of the polynomial $2p^2q - 3pq + q^2$ ?
How do you state the degree of the polynomial $4a^2b^3 + 2ab^2 – 10$ ?
How do you find degree in a polynomial $x^6yz - x^8 y^2 -3x^5y^2 z^3$ ?
How do you find the degree of $4x+6xy-3x^4y+5$ ?
How do you find the degree of $m^3 n^3 + 6mn^2 - 14m^3n$ ?
How do you find the degree of the polynomial $3x^2+8x^3-9x-8$ ?
How do I find the degree of a polynomial $2x^2-x+3$ ?
How do you find the degree: $q^3 + q^3r^4s^5 - s^2$ ?
What is the degree of the polynomial $3x^2y-5x^2$ ?
How do you state the degree of the polynomial $xy^2 + 3xy - 7 + y$ ?
How do I find the degree of these polynomials $4x^2 + 12xyz$ ?
What is the degree of the polynomial $x^5 + 1 - 3x^4 + 3x^9 - 2x$ ?
What is the coefficient of the term of degree 2 in the polynomial $7x^5 + 3x^2 - x^6 + 4 - 5x$ ?
How do you identify the degree of each term of the polynomial and the degree of the polynomial $-7x^3+9x^2+3x+5$ ?
How do you state the degree and leading coefficient of the polynomial function $F(x) = 14+ 13x^4 - 6x - 14x^3 -8x^2$ ?
What is the degree of $3x^4y^2 - 5x^2y + 3$ ?
What is the degree of $2x^5y^2$ ?
What is the degree of $-12v - 19$ ?
What is the degree of $5x^2+2x+1$ ?
What is the degree of $7x^2y^2 - 8xy^3 - 11x^3y$ ?
What is the degree of $2(x+6)^2(x-6)^3=0$ ?
What is the degree of $-5x^2(x-7)(x+1)^3=0$ ?
What is the degree of $x^2 + 2x + 3$ ?
What is the degree of $16x^4yz + 12x^2y^3z - 24x^3y^2z - 18xy^4z$ ?
What is the degree of $9x^4+3x^3+7x^2+8$ ?
What is the degree of $3x^3+6x^2-2x-4$ ?
What is the end behavior of $f(x)=4x^7-3x^2+5x-2$ ?
What is the end behavior of $f(x)=-2x^3+5x^2$ ?
What is the end behavior of $f(x)=6x^3+1$ ?
What is the end behavior of $f(x)=-10x^3$ ?
What is the end behavior of $f(x)=-x^6+2x^3-x$ ?
What is the end behavior of $f(x)=x^5+2x^2$ ?
What is the end behavior of $f(x)=-3x^5-4x^2+3$ ?
What is the end behavior of $f(x)=-6x^3+10x$ ?
What is the end behavior of $f(x)=x^4-5x^3+x-1$ ?
How do you describe the end behavior of $f(x)=x^3-4x^2+7$ ?
How do you describe the end behavior of $f(x)=x^3-4x^2+4$ ?
How do you describe the end behavior of $f(x)=x^5-4x^3+5x+2$ ?
How do you describe the end behavior of $f(x)=2x^2+12x+12$ ?
How do you describe the end behavior of $f(x)=x^2-8x+18$ ?
How do you find the maximum number of turns the graph $f(x)=-x^2-1$ make?
How do you sketch the general shape of $f(x)=x^3-2x^2+1$ using end behavior?
How do you sketch the general shape of $f(x)=-x^4+3x^2-2-5x$ using end behavior?
How do you sketch the general shape of $f(x)=-x^5+3x^3+2$ using end behavior?
How do you sketch the general shape of $f(x)=-x^3+10x^2-33x+32$ using end behavior?
How do you describe the end behavior for $f(x)=x^3+10x^2+32x+34$ ?
How do you describe the end behavior for $f(x)=-x^4+x^2+2$ ?
How do you describe the end behavior for $f(x)=x^3-3x^2+1$ ?
How do you describe the end behavior for $f(x)=-x^5+4x^3-5x-4$ ?
How do you describe the end behavior for $f(x)=x^4-3x^2-3x+4$ ?
How do you describe the end behavior for $f(x)=-x^2-8x-15$ ?
How do you describe the end behavior for $f(x)=x^4-x^2-2$ ?
How do you describe the end behavior for $f(x)=x^5-4x^3+x+1$ ?
How do you describe the end behavior for $f(x)=-x^3+3x^2-4$ ?
How do you describe the end behavior for $f(x)=-x^5+4x^3-2x-2$ ?
How do you sketch the general shape of $f(x)=x^3-x^2+4$ using end behavior?
How do you sketch the general shape of $f(x)=x^5-3x^3+2x+4$ using end behavior?
How do you sketch the general shape of $f(x)=-x^4+3x^2-2x-4$ using end behavior?
How do you sketch the general shape of $f(x)=-x^3+3x^2-2$ using end behavior?
How do you sketch the general shape of $f(x)=x^3-3x^2+4$ using end behavior?
How do you sketch the general shape of $f(x)=x^3-10x^2+33x-38$ using end behavior?
How do you sketch the general shape of $f(x)=-x^3+x^2+1$ using end behavior?
How do you sketch the general shape of $f(x)=x^4-2x^2+x-2$ using end behavior?
How do you sketch the general shape of $f(x)=-x^3+2x^2+1$ using end behavior?
How do you sketch the general shape of $f(x)=-x^3-6x^2-9x-4$ using end behavior?
How do you sketch the general shape of $f(x)=-x^3+4x^2-7$ using end behavior?
How do you sketch the general shape of $f(x)=-x^3-4x^2+3$ using end behavior?
How do you sketch the general shape of $f(x)=x^3-4x^2+2$ using end behavior?
How do you sketch the general shape of $f(x)=x^3-4x^2+7$ using end behavior?
How do you describe the end behavior of $y=4x^5+2x^4-3x-1$ ?
How do you describe the end behavior of $y=-x^6+x^4-5x^2+4$ ?
How do you describe the end behavior of $y=8-x^3-2x^4$ ?
How do you describe the end behavior of $f(x)=x^10-x^9+5x^8$ ?
How do you describe the end behavior of $f(x)=-1/x^3+2$ ?
How do you determine the intervals for which the function is increasing or decreasing given $f(x)=(x+3)^2-4$ ?
How do you determine the intervals for which the function is increasing or decreasing given $f(x)=x/(x^2+1)$ ?
How do you determine the intervals for which the function is increasing or decreasing given $f(x)=x^3+3x^2-9x$ ?
How do you determine the intervals for which the function is increasing or decreasing given $f(x)=-x^3-2x+1$ ?
How do you determine the intervals for which the function is increasing or decreasing given $f(x)=1/(x+1)-4$ ?
How do you determine the intervals for which the function is increasing or decreasing given $f(x)=(x^2+5)/(x-2)$ ?
How do you determine the intervals for which the function is increasing or decreasing given $f(x)=abs(x^2-4)$ ?
How do you determine the intervals for which the function is increasing or decreasing given $f(x)=(2absx-3)^2+1$ ?
If you have a polynomial where the leading coefficient is positive and the degree is odd, what is the end behavior?
What is the end behavior of $f(x)=-5x^4-2x-7$ ?
How do you find the degree and leading coefficient of the polynomial $a^3+6a+14$ ?
How do you find the degree and leading coefficient of the polynomial $5m^2+8m^5-2$ ?
How do you find the degree and leading coefficient of the polynomial $5t^4+t^3-7$ ?
How do you find the degree and leading coefficient of the polynomial $3x^7-4x^5+x^3$ ?
How do you find the degree and leading coefficient of the polynomial $9a^2+5a^3-10$ ?
How do you find the degree and leading coefficient of the polynomial $14b-25b^6$ ?
How do you find the degree and leading coefficient of the polynomial $p^5+7p^3-p^6$ ?
How do you find the degree and leading coefficient of the polynomial $14y+30+y^2$ ?
How do you find the end behavior and state the possible number of x intercepts and the value of the y intercept given $f(x)=x^2+3x-1$ ?
How do you find the end behavior and state the possible number of x intercepts and the value of the y intercept given $h(x)=-7x^4+2x^3-3x^2+6x+4$ ?
How do you find the end behavior and state the possible number of x intercepts and the value of the y intercept given $y=x^2-4$ ?
How do you find the end behavior and state the possible number of x intercepts and the value of the y intercept given $y=x^3-4x$ ?
How do you find the end behavior and state the possible number of x intercepts and the value of the y intercept given $y=-x^3-4x$ ?
How do you find the end behavior and state the possible number of x intercepts and the value of the y intercept given $y=x^4+2x^2+1$ ?
How do you find the end behavior and state the possible number of x intercepts and the value of the y intercept given $y=x^5-2x^4-3x^3+5x^2+4x-1$ ?
How do you find the end behavior and state the possible number of x intercepts and the value of the y intercept given $y=x^5-1$ ?
How do you find the end behavior and state the possible number of x intercepts and the value of the y intercept given $y=x(x+1)^2(x+4)^2$ ?
How do you determine the end behavior of $f(x)=1/3x^3+5x$ ?
How do you determine the end behavior of $f(x)=1-x^6$ ?
How do you determine the end behavior of $f(x)=-2.1x^5+4x^3-2$ ?
How do you determine the end behavior of $f(x)=2x^5-5x+7.5$ ?
How do you determine the end behavior of $f(x)=6-2x+4x^2-5x^3$ ?
How do you determine the end behavior of $f(x)=(3x^4-2x+5)/4$ ?

Polynomial Functions of Higher Degree

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Graphing Polynomial Functions
End Behavior
Zeros
Intermediate Value Theorem
Polynomial Functions of Higher Degree on a Graphing Calculator

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End Behavior

Key Questions

Answer:

Explanation:

Questions

Polynomial Functions of Higher Degree