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Questions and Answers
What are the values that we would get for the equation x - 7 = 0?
What are the values that we would get for the equation x - 7 = 0?
- 7 (correct)
- -1
- -7 (correct)
- 1
What is an even function?
What is an even function?
A function that is symmetrical over the Y-axis.
What defines an odd function?
What defines an odd function?
A function that is symmetrical over the origin.
How do you determine if a function is even or odd?
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?
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?
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.
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