Write a Function Based on the Given Parent Function and the Transformations

question 54

Multiple Choice

Write a function based on the given parent function and the transformations in the given order.
-Parent function: $y = x ^ { 3 }$
1. Shift 6.8 units to the right.
2. Reflect across the y-axis.
3. Shift downward 5.2 units.

• A) \(y = ( - x + 6.8 ) ^ { 3 } + 5.2\)
• B) \(y = - ( x + 6.8 ) ^ { 3 } + 5.2\)
• C) \(y = ( - x - 6.8 ) ^ { 3 } - 5.2\)
• D) \(y = - ( x - 6.8 ) ^ { 3 } - 5.2\)

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Definitions:

Fleming's Left-hand Generator Rule

A rule used to predict the direction of movement in a motor, the direction of induced current, or the force on a conductor in a magnetic field, based on the thumb, forefinger, and middle finger of the left hand.

Time Constant

The time required for a system to charge or discharge to approximately 63.2% of its maximum value, characteristic of both RC and RL circuits.

R-L

Refers to a circuit that contains both resistance (R) and inductance (L), affecting the phase and amplitude of the circuit's response to an AC input.

Exponential Curves

Graphs representing exponential functions, showing how values can grow rapidly due to constant proportionality rates.