4. Polynomial Functions

Understanding Polynomial Functions

Open Question
Graph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing. See Example 1. ƒ(x)=1/2(x-2)^2+4
Open Question
For each polynomial function, identify its graph from choices A–F. ƒ(x)=-(x-2)(x-5)
Open Question
In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. f(x)=(x^2+7)/x^3
Multiple Choice
Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient. $f\left(x\right)=4x^3+\frac12x^{-1}-2x+1$
Multiple Choice
Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient. $f\left(x\right)=2+x$
Multiple Choice
Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient. $f\left(x\right)=3x^2+5x+2$
Multiple Choice
Determine the end behavior of the given polynomial function. $f\left(x\right)=x^2+4x+x+7x^3$
Multiple Choice
Match the given polynomial function to its graph based on end behavior. $f\left(x\right)=-2x^3+x^2+1$
Multiple Choice
Find the zeros of the given polynomial function and give the multiplicity of each. State whether the graph crosses or touches the x-axis at each zero. $f\left(x\right)=2x^4-12x^3+18x^2$
Multiple Choice
Find the zeros of the given polynomial function and give the multiplicity of each. State whether the graph crosses or touches the x-axis at each zero. $f\left(x\right)=x^2\left(x-1\right)^3\left(2x+6\right)$
Multiple Choice
Determine the maximum number of turning points for the given polynomial function. $f\left(x\right)=6x^4+2x$