4. Polynomial Functions

Graphing Polynomial Functions

4. Polynomial Functions

Graphing Polynomial Functions

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Identifying Intervals of Unknown Behavior

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Identifying Intervals of Unknown Behavior

Graphing Polynomial Functions

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Attributes of Polynomial Functions

Even and Odd Symmetries

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Multiple Choice

Based on the known points plotted on the graph, determine what intervals the graph should be broken into.

Plotted points are: $\left(-3,0\right),$ $\left(0,1\right),\left(2,0\right),$ & $\left(5,0\right)$

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Multiple Choice

Graph the polynomial function. Determine the domain and range. $f\left(x\right)=\left(3x+2\right)\left(x-1\right)^2$

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Textbook 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

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Textbook Question

In Exercises 11–14, identify which graphs are not those of polynomial functions.

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Textbook 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) = 4x - x^3

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Textbook Question

In Exercises 33–40, use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=x^3−4x^2+2; between 0 and 1

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Textbook Question

Graph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. ƒ(x)=2x^3-5x^2-x+6

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Textbook Question

Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. See Example 2. ƒ(x) = -2x^2 - 8x - 7

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Textbook Question

Graph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. ƒ(x)=x^4+3x^3-3x^2-11x-6

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Textbook Question

If the given term is the dominating term of a polynomial function, what can we conclude about each of the following features of the graph of the function? (a)domain (b)range (c)end behavior (d)number of zeros (e)number of turning points -9x6

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Textbook Question

For each polynomial function, identify its graph from choices A–F. ƒ(x)=-(x-2)(x-5)

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Textbook Question

Show that the real zeros of each polynomial function satisfy the given conditions. See Example 6. ƒ(x)=x^4+x^3-x^2+3; no real zero less than -2

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4. Polynomial Functions

Graphing Polynomial Functions

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Learn with other creators

Practice this topic