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Polynomial Functions Graphing Mastery Quiz

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Polynomial Functions Graphing Mastery Quiz

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Questions and Answers

What is the end behavior of the graph of $y = x^2$ as $x$ approaches positive infinity?

The end behavior is up, as $x$ approaches positive infinity, $y$ approaches negative infinity.

The end behavior is down, as $x$ approaches positive infinity, $y$ approaches negative infinity.

The end behavior is up, as $x$ approaches positive infinity, $y$ approaches positive infinity. (correct)

The end behavior is down, as $x$ approaches positive infinity, $y$ approaches positive infinity.

How is the end behavior of an even function described?

It has a negative slope.

It is symmetrical about the x-axis.

It has a positive slope.

It is symmetrical about the y-axis. (correct)

What type of function is $y = x^2$?

Neither even nor odd function

Odd function

Even function (correct)

Both even and odd function

What happens to the values of $y$ as $x$ approaches negative infinity for the graph of $y = x^2$?

<p>As $x$ approaches negative infinity, $y$ approaches positive infinity.</p> Signup and view all the answers

What is the degree of the function $y = x^2$?

<p>2</p> Signup and view all the answers

Study Notes

End Behavior of the Graph of ( y = x^2 )

As ( x ) approaches positive infinity, ( y = x^2 ) also approaches positive infinity, indicating that the graph rises without bound.
The end behavior mirrors that of a typical quadratic function, characterized by a U-shaped curve.

Characteristics of Even Functions

Even functions exhibit symmetry about the y-axis.
For all even functions, the end behavior as ( x ) approaches both positive and negative infinity is the same.

Type of Function

The function ( y = x^2 ) is classified as a quadratic function due to its highest degree being two.

End Behavior as ( x ) Approaches Negative Infinity

As ( x ) approaches negative infinity, the values of ( y = x^2 ) still approach positive infinity, maintaining the upward trend of the graph.

Degree of the Function

The degree of the function ( y = x^2 ) is two, which defines its quadratic nature and affects the nature of its end behavior and graph shape.

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Description

Graphing Polynomial Functions Quiz: Test your knowledge of graphing polynomial functions by understanding end behavior, multiplicity, and finding zeros. Learn how to plot even functions such as y = x^2 and grasp the concept of symmetry around the y-axis. Perfect your graphing skills with this informative quiz!