5 Questions
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 positive infinity.
How is the end behavior of an even function described?
It is symmetrical about the y-axis.
What type of function is $y = x^2$?
Even function
What happens to the values of $y$ as $x$ approaches negative infinity for the graph of $y = x^2$?
As $x$ approaches negative infinity, $y$ approaches positive infinity.
What is the degree of the function $y = x^2$?
2
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.
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!
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