Math Problem Statement
Which of the following functions is an even function?
Solution
An even function is a function that satisfies the condition for all in the domain of the function. This means that the function is symmetric with respect to the y-axis.
Let's analyze each of the given functions:
-
:
- This is not equal to the original function , so this function is not even.
-
:
- This is equal to the original function , so this function is even.
-
:
- This is not equal to the original function , so this function is not even.
-
:
- This is not equal to the original function , so this function is not even.
Conclusion: The correct answer is the second function , which is an even function.
Would you like more details on this or have any further questions?
Here are some related questions you might consider:
- What is the definition of an odd function?
- Can a function be both even and odd? If so, under what conditions?
- How do you determine if a polynomial is even or odd?
- What is the symmetry of odd functions?
- Can an even function have a non-zero linear term (i.e., a term with )?
- What is the general form of an even polynomial function?
- How do transformations (like translations or reflections) affect the evenness of a function?
- How can you verify whether a given trigonometric function is even or odd?
Tip: When determining whether a function is even, pay close attention to the exponents of each term. If all exponents are even, the function is likely to be even.
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Math Problem Analysis
Mathematical Concepts
Even function
Symmetry
Formulas
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Theorems
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Suitable Grade Level
Grades 10-12
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