Reciprocal Squared Functions Flashcards

Questions and Answers

What is the Reciprocal Squared Equation?

y = 1/x^2

What is the behavior of the ROC Reciprocal Squared?

Increases at an increasing rate, decreases at a decreasing rate.

Describe the behavior of the Reciprocal Squared function.

Increasing than decreasing

What are the positive intervals of the Reciprocal Squared function?

(negative infinity to 0) and (0 to infinity) Signup and view all the answers

The Reciprocal Squared function has a minimum or maximum.

False Signup and view all the answers

The Reciprocal Squared function has negative intervals.

False Signup and view all the answers

Study Notes

Reciprocal Squared Equation

Defined by the equation: y = 1/x²
Represents a fundamental relationship in mathematics with key features.

Reciprocal Squared Parent Function Graph

Typically exhibits a hyperbolic shape, established by the equation.
The graph approaches both the x-axis and y-axis but never intersects them (asymptotic behavior).

Rate of Change (ROC) for Reciprocal Squared

The function increases at an increasing rate as x approaches 0 from the negative side and decreases at a decreasing rate as x approaches 0 from the positive side.
Indicates a responsiveness of the function's slope that is accentuated near the origin.

Behavior of Reciprocal Squared

The function first increases as x moves from negative infinity toward 0, reaching a peak value.
After reaching its peak, the function subsequently decreases as x moves from 0 to positive infinity.

Positive Intervals of Reciprocal Squared

The function is positive in two intervals:
- From negative infinity to 0 (non-inclusive of zero)
- From 0 to positive infinity (non-inclusive of zero).

Minimum or Maximum for Reciprocal Squared

No minimum or maximum exists within the domain of the function.
The graph continually approaches the x-axis without touching it, demonstrating an open-ended behavior.

Negative Intervals of Reciprocal Squared

There are no negative intervals where the function yields negative values.
The function remains positive throughout its defined intervals.

Description

Explore the essential concepts of reciprocal squared functions through these flashcards. Each card covers key terms and definitions related to the reciprocal squared equation, its graph, and related behaviors. Perfect for students looking to deepen their understanding of this mathematical concept.