Reciprocal Parent Function Flashcards

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?

Constant rate

Decreases at an increasing rate (correct)

Increases at an increasing rate

Decreases at a decreasing rate (correct)

The Reciprocal Parent Function is strictly increasing.

False Signup and view all the answers

Does the Reciprocal Parent Function have a minimum or maximum?

False Signup and view all the answers

What are the positive intervals for the Reciprocal Parent Function?

(0 to infinity) Signup and view all the answers

What are the negative intervals for the Reciprocal Parent Function?

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

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).

Description

Test your understanding of the reciprocal parent function with these flashcards. Each card covers essential concepts such as the function equation, graph characteristics, and its behavior. Perfect for reinforcing key ideas in algebra.