Questions and Answers
What is Absolute Value?
The distance a number is from zero on a number line. ALWAYS POSITIVE
What is the Absolute Value Function?
A piecewise function with a V-shaped graph that opens up or down. The parent function is y = | x |, where f(x) ≥ 0 for all values of x.
What is an extraneous solution?
An apparent solution that must be rejected because it does not satisfy the original equation.
What does the expression -|x| represent?
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What does the function y = f(-x) do?
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What does the function y = f(x + c) do?
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What does the function y = f(x - c) do?
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What does the function y = 1/c * f(x) do?
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What does the function y = c * f(x) do?
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What does the function y = f(1/c x) do?
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What does the function y = f(c x) do?
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What does the expression y = |-x| indicate?
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Study Notes
Absolute Value Concepts
- Absolute value represents the distance of a number from zero on a number line and is always positive.
Absolute Value Function
- Forms a piecewise function yielding a V-shaped graph that opens upwards or downwards.
- The parent function is y = |x|, where f(x) is non-negative (f(x) ≥ 0) for all x values.
Extraneous Solution
- Refers to a solution that appears to be valid but does not satisfy the initial equation and must be discarded.
Graph Transformations
- Reflection Over X-Axis: The transformation of -|x| indicates a reflection of the graph across the x-axis.
- Reflection Over Y-Axis: The expression y = f(-x) reflects the graph across the y-axis.
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Horizontal Shifts:
- y = f(x + c) results in shifting the graph left by c units.
- y = f(x - c) shifts the graph right by c units.
Vertical Transformations
- Vertical Compression: The equation y = (1/c) * f(x) compresses the graph vertically.
- Vertical Stretch: The function y = c * f(x) stretches the graph vertically.
Horizontal Transformations
- Horizontal Stretch: The transformation y = f(1/c * x) applies a horizontal stretch to the graph.
- Horizontal Compression: The equation y = f(c * x) indicates a horizontal compression of the graph.
Additional Reflection
- The expression y = |-x| shows reflection around the y-axis, providing symmetry relative to the y-axis.
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Description
This flashcard set focuses on essential concepts of absolute value in algebra. It includes definitions and explanations of key terms such as absolute value, absolute value function, and extraneous solutions. Perfect for students looking to reinforce their understanding of absolute value in mathematical contexts.
