Questions and Answers
Which graph represents an even function?
If f(x) = (x^m + 9)^2, then f(x) is an even function for all even values of m.
True
Which graph shows rotational symmetry?
If f(x) consists of 14 points and six of the points lie in Quadrant I, what is the greatest number of points that can lie in Quadrant II if f(x) is an odd function?
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Which of the following is an even function?
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If f(x) is an odd function and the graph of f(x) includes points in Quadrant IV, it must include points in Quadrant II.
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How would you describe f(x), graphed on the coordinate plane, if it is an odd function?
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Which of the following is an even function?
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How can you determine whether f(x) = x^4 - x^3 is an even function?
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How can you determine whether f(x) = x^3 + 5x + 1 is an even function?
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Study Notes
Even and Odd Functions
- An even function is symmetric about the y-axis, meaning f(x) = f(-x).
- Example of an even function: ( f(x) = 7 ) and ( f(x) = |x| ).
- If ( f(x) = (x^m + 9)^2 ), it is even for any even value of m.
Graphical Representation
- Graph C represents an even function.
- Graph A shows rotational symmetry—a graph that can be rotated around a point and appear unchanged.
Quadrant Analysis
- For a graph of an odd function consisting of 14 points where 6 points are in Quadrant I, the maximum in Quadrant II is one point.
- If an odd function's graph contains points in Quadrant IV, it must also contain points in Quadrant II.
Function Evaluation
- To determine if ( f(x) = x^4 - x^3 ) is even, evaluate if ( (-x)^4 - (-x)^3 ) equals ( x^4 - x^3 ).
- For ( f(x) = x^3 + 5x + 1 ), check if ( (-x)^3 + 5(-x) + 1 ) equals ( x^3 + 5x + 1 ).
Conclusion
- Understanding the characteristics of even and odd functions is crucial for graph interpretation and evaluation.
- Recognizing the symmetry properties of the graphs aids in classifying them efficiently.
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Description
Test your knowledge of symmetry with these flashcards! This quiz focuses on identifying even functions, graphs with rotational symmetry, and characteristics of mathematical functions. Perfect for students learning about symmetry in mathematics.
