4. Polynomial Functions

Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $f\left(x\right)=-5x^4+7x^2-x+9$

Use one of the end behavior diagrams below, to describe the end behavior of the graph of each polynomial function.

$\text{ƒ}\left(x\right)=-4x^3+3x^2-1$

Use an end behavior diagram, as shown below, to describe the end behavior of the graph of each polynomial function. ƒ(x)=4x⁷-x⁵+x³-1

In Exercises 25–26, graph each polynomial function. $f\left(x\right)=2x^2(x-1{)}^3(x+2)$

Use an end behavior diagram, as shown below, to describe the end behavior of the graph of each polynomial function. ƒ(x)=9x⁶-3x⁴+x²-2

Find the zeros for each polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero. f(x)=2(x−5)(x+4)²

Find the zeros for each polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero. f(x)=3(x+5)(x+2)²

Use an end behavior diagram, as shown below, to describe the end behavior of the graph of each polynomial function. ƒ(x)=10x⁶-x⁵+2x-2

In Exercises 25–26, graph each polynomial function. $f\left(x\right)=-x^3(x+4{)}^2(x-1)$

Use an end behavior diagram, as shown below, to describe the end behavior of the graph of each polynomial function. ƒ(x)=3+2x-4x²-5x¹⁰

Find the zeros for each polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero. f(x)=−3(x+1/2)(x−4)³

Use an end behavior diagram, as shown below, to describe the end behavior of the graph of each polynomial function. ƒ(x)=7+2x-5x²-10x⁴

Find the zeros for each polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero. $f\left(x\right)=x^3+7x^2-4x-28$

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=-2x(x-3)(x+2)

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=-x(x+1)(x-1)