Topics
3. Polynomial Expressions, Equations, & Functions
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United States of AmericaVirginia
Algebra 2

3.04 Characteristics of polynomial functions

Lesson
Practice
Adaptive
Worksheet

Interactive practice questions

Consider the graph of the quartic function, $f\left(x\right)$f(x), graphed below.

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A Coordinate Plane has x-axis ranging from $-10$−10 to $10$10 and y-axis ranging $-6$−6 to $6$6. A curve is plotted on the Coordinate Plane. The curve moves downward from left to right until it reaches one turning point at $x=-4$x=−4. From this point $x=-4$x=−4, the curve moves upward until it reaches another turning point at $x=-1$x=−1. From this turning point $x=-1$x=−1, the curve moves downward, until it reaches another turning point at $x=2$x=2. From this point $x=2$x=2, the curve moves upward extending beyond the visible part of the graph. All turning points are not marked and not explicitly labeled. All coordinates are also not explicitly labeled.
a

What are the regions of the domain where $f\left(x\right)$f(x) is increasing?

Write all of the regions in interval notation separated by commas.

b

What are the regions of the domain where $f\left(x\right)$f(x) is decreasing?

Write all of the regions in interval notation separated by commas.

Easy
1min

Consider the function $g\left(x\right)=-\left(x-3\right)^2\left(x+3\right)^2$g(x)=−(x−3)2(x+3)2 drawn below.

Easy
1min

Consider the function $f\left(x\right)$f(x) shown in the graph below.

Easy
1min

Consider the adjacent graph:

Easy
< 1min
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Outcomes

A2.F.2

The student will investigate and analyze characteristics of square root, cube root, rational, polynomial, exponential, logarithmic, and piecewise-defined functions algebraically and graphically.

A2.F.2a

Determine and identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically, including graphs with discontinuities.

A2.F.2b

Compare and contrast the characteristics of square root, cube root, rational, polynomial, exponential, logarithmic, and piecewise-defined functions.

A2.F.2c

Determine the intervals on which the graph of a function is increasing, decreasing, or constant.

A2.F.2d

Determine the location and value of absolute (global) maxima and absolute (global) minima of a function.

A2.F.2e

Determine the location and value of relative (local) maxima or relative (local) minima of a function.

A2.F.2f

For any value, x, in the domain of f, determine f(x) using a graph or equation. Explain the meaning of x and f(x) in context, where applicable.

A2.F.2g

Describe the end behavior of a function.

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