End Behavior

Problems

Describe the end behavior of the following polynomial functions.

\(\textbf{1)}\) \( f(x)=x^4+2x^3-4x+2 \)

 

\(\textbf{2)}\) \( f(x)=6x^3+x^2-12 \)

 

\(\textbf{3)}\) \( f(x)=-2x^2+3 \)

 

\(\textbf{4)}\) \( f(x)=-8x^2-3x+5 \)

 

\(\textbf{5)}\) \( f(x)=4x \)

 

\(\textbf{6)}\) \( f(x)=-x \)

 

\(\textbf{7)}\) \( f(x)= -4x^3-20x^2+3x-8 \)

 

\(\textbf{8)}\) \( f(x)=x^4+2x^3-4x+2 \)

 

\(\textbf{9)}\) \( f(x)=6x^3+x^2-12 \)

 

\(\textbf{10)}\) \( f(x)=-2x^2+3 \)

 

 

See Related Pages\(\)

\(\bullet\text{ Adding and Subtracting Polynomials}\)
\(\,\,\,\,\,\,\,\,(4d+7)−(2d−5)…\)
\(\bullet\text{ Multiplying Polynomials}\)
\(\,\,\,\,\,\,\,\,(x+2)(x^2+3x−5)…\)
\(\bullet\text{ Dividing Polynomials}\)
\(\,\,\,\,\,\,\,\,(x^3-8)÷(x-2)…\)
\(\bullet\text{ Dividing Polynomials (Synthetic Division)}\)
\(\,\,\,\,\,\,\,\,(x^3-8)÷(x-2)…\)
\(\bullet\text{ Synthetic Substitution}\)
\(\,\,\,\,\,\,\,\,f(x)=4x^4−3x^2+8x−2…\)
\(\bullet\text{ End Behavior}\)
\(\,\,\,\,\,\,\,\, \text{As } x\rightarrow \infty, \quad f(x)\rightarrow \infty \)
\(\,\,\,\,\,\,\,\, \text{As } x\rightarrow -\infty, \quad f(x)\rightarrow \infty… \)
\(\bullet\text{ Completing the Square}\)
\(\,\,\,\,\,\,\,\,x^2+10x−24=0…\)
\(\bullet\text{ Quadratic Formula and the Discriminant}\)
\(\,\,\,\,\,\,\,\,x=-b \pm \displaystyle\frac{\sqrt{b^2-4ac}}{2a}…\)
\(\bullet\text{ Complex Numbers}\)
\(\,\,\,\,\,\,\,\,i=\sqrt{-1}…\)
\(\bullet\text{ Multiplicity of Roots}\)
\(\,\,\,\,\,\,\,\,\)Thumbnail for Multiplicity of Roots\(…\)
\(\bullet\text{ Rational Zero Theorem}\)
\(\,\,\,\,\,\,\,\, \pm 1,\pm 2,\pm 3,\pm 4,\pm 6,\pm 12…\)
\(\bullet\text{ Descartes Rule of Signs}\)
\(\,\)
\(\bullet\text{ Roots and Zeroes}\)
\(\,\,\,\,\,\,\,\,\text{Solve for }x. 3x^2+4x=0…\)
\(\bullet\text{ Linear Factored Form}\)
\(\,\,\,\,\,\,\,\,f(x)=(x+4)(x+1)(x−3)…\)
\(\bullet\text{ Polynomial Inequalities}\)
\(\,\,\,\,\,\,\,\,x^3-4x^2-4x+16 \gt 0…\)

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