Podcast
Questions and Answers
What is the end behavior of the graph of $y = x^2$ as $x$ approaches positive infinity?
How is the end behavior of an even function described?
What type of function is $y = x^2$?
What happens to the values of $y$ as $x$ approaches negative infinity for the graph of $y = x^2$?
Signup and view all the answers
What is the degree of the function $y = x^2$?
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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!
