4. Polynomial Functions

Understanding Polynomial Functions

Multiple Choice
Based ONLY on the maximum number of turning points, which of the following graphs could NOT be the graph of the given function? $f\left(x\right)=x^3+1$
Multiple Choice
The given term represents the leading term of some polynomial function. Determine the end behavior and the maximum number of turning points. $4x^5$
Open Question
In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. f(x)=5x^2+6x^3
Open Question
In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. g(x)=7x^5−πx^3+1/5 x
Open Question
In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. h(x)=7x^3+2x^2+1/x
Open Question
In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. f(x)=x^1/2 −3x^2+5
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)=2x^4
Open Question
In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. f(x)=(x^2+7)/3
Open Question
In Exercises 10–13, use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with its graph. [The graphs are labeled (a) through (d).] f(x) = -x^3 + x^2 + 2x
Open Question
In Exercises 10–13, use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with its graph. [The graphs are labeled (a) through (d).] f(x) = x^6 -6x^4 + 9x^2
Open Question
In Exercises 11–14, identify which graphs are not those of polynomial functions.
Open Question
In Exercises 11–14, identify which graphs are not those of 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)=1/3(x+3)^4-3
Open Question
Graph the following on the same coordinate system. (a) y = x^2 (b) y = 3x^2 (c) y = 1/3x^2 (d) How does the coefficient of x2 affect the shape of the graph?
Open Question
In Exercises 19–24,(a) Use the Leading Coefficient Test to determine the graph's end behavior.(b) Determine whether the graph has y-axis symmetry, origin symmetry, or neither.(c) Graph the function.f(x) = x^3 - x^2 - 9x + 9