Math Problem Statement
What is the graph of the function \( f(x) = x^5 \) like?
Solution
This is the graph of the function . The curve shows key characteristics of odd-degree polynomials with positive leading coefficients:
- Symmetry: The graph is symmetric with respect to the origin, illustrating odd symmetry (rotational symmetry by 180 degrees).
- Shape: The general shape is similar to a cubic function, but with steeper slopes as moves away from zero.
- Behavior at Zero: The graph passes through the origin, since .
- End Behavior: As approaches infinity, also goes to infinity; as approaches negative infinity, ( f
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Polynomials
Odd Functions
End Behavior of Functions
Formulas
f(x) = x^5
Theorems
Odd Function Symmetry
End Behavior of Odd-Degree Polynomials
Suitable Grade Level
Grades 9-12