Questions and Answers
What are the values that we would get for the equation x - 7 = 0?
What is an even function?
A function that is symmetrical over the Y-axis.
What defines an odd function?
A function that is symmetrical over the origin.
How do you determine if a function is even or odd?
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When dealing with a graph, what do you need to remember about lines that hit zero?
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How do you find the stretch or compression of a graph?
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Study Notes
Piecewise Functions Overview
- Piecewise functions consist of multiple sub-functions, each defined on a specific interval.
- These functions require testing specific intervals to determine which equation to use.
Function Equations and Solutions
- For the equation g(x)=x²-6x-7, solutions can be derived by factoring or using the quadratic formula.
- The terms -7 and 1 can be used to manipulate the equation to isolate x.
Even Functions
- A function is classified as even if it exhibits symmetry over the Y-axis.
- Even functions maintain the property f(-x) = f(x), meaning substituting -x into the equation yields the same output.
Odd Functions
- A function is defined as odd if it is symmetric about the origin (0,0).
- Use a straight line through the origin to assess symmetry; if the graph reflects through the origin, it's odd.
Determining Function Symmetry
- To check if a function is even or odd, replace x with -x:
- If the result equals the original function, it’s even.
- If it results in the negative of the original function, it’s odd.
- If neither condition is satisfied, the function is neither even nor odd.
Graphing Considerations
- When graphs intersect the x-axis but do not extend below it, separate equations must be created for positive and negative sections.
- For instance, input intervals like (-∞, 0) ∪ (0, 4) to represent the distinct sections of the graph accurately.
Analyzing Stretch and Compression
- To understand vertical transformations in the graph, sketch the baseline function and observe changes in Y values between two points with the same corresponding X.
- By comparing these Y values, the degree of stretch or compression can be determined visually.
Studying That Suits You
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Description
Prepare for your Algebra II test with these flashcards focused on piecewise functions. Each card presents key concepts and definitions, helping you reinforce your understanding of even functions and related equations. Perfect for quick study sessions and revision.
