Questions and Answers
What is the Reciprocal Parent Function Equation?
Reciprocal Parent Function Equation
What is the Reciprocal Parent Function Graph?
Reciprocal Parent Function Graph
What does ROC refer to?
The Reciprocal Parent Function is strictly increasing.
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Does the Reciprocal Parent Function have a minimum or maximum?
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What are the positive intervals for the Reciprocal Parent Function?
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What are the negative intervals for the Reciprocal Parent Function?
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Study Notes
Reciprocal Parent Function Overview
- The reciprocal parent function is represented by the equation f(x) = 1/x.
- This function is characterized by its hyperbolic shape, with two distinct branches.
Reciprocal Parent Function Graph
- The graph approaches the x-axis and y-axis but never touches either, demonstrating asymptotic behavior.
- The branches exist in the first quadrant (positive values) and the third quadrant (negative values).
Rate of Change (ROC)
- The rate of change for the reciprocal parent function decreases at a decreasing rate as x moves away from zero.
- Conversely, it decreases at an increasing rate as x approaches zero from either side.
General Behavior
- The reciprocal parent function is strictly decreasing across its entire domain.
- As x approaches zero, f(x) approaches either positive or negative infinity, depending on the direction of approach.
Extremum Points
- The reciprocal parent function does not have a minimum or maximum value.
- It continues infinitely in both the positive and negative y-directions.
Positivity and Negativity of Intervals
- The function is positive in the interval from 0 to infinity (x > 0).
- The function is negative in the interval from negative infinity to 0 (x < 0).
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