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Step-by-step explanation:
The translations of the typical functions are
Where a is the vertical translation,
If a is greater than 1 or less than -1, we have a vertical stretch
If a is between -1 and 1 , we have a vertical compressions or shrink.
If a is negative, we have a negative reflection across the x axis.
If b is greater than 1 or less than -1, we have a horizontal compression or shrink
If b is between -1 and 1, we have a horizontal stretch
If b is negative, we have a reflection about the y axis,
If c is negative, we have a translation to the right c units
If c is positive, we have a translation to the left c units
If d is positive, we have a translation upward d units
If d is negative, we have a translation downward d units.
Here in this problem, our parent function is x^3.
So I would do the following transformations.
- Reflect about the x axis
- Vertical Shrink by a factor of 1/2
- Horizontal Shrink by a factor of 3
- Shift to the left 4 units
- Shift downward 8 units.
(7x + 4)(7x + 4) and (x – 9)(x – 9) are Perfect square trinomial. (5x + 3)(5x – 3) and (–3x – 6)(–3x + 6) shows the Difference of squares.
<h3>What is a perfect square?</h3>A perfect square is a number system that can be expressed as the
square of a given number from the same system.
The following are the answers
(5x + 3)(5x – 3) Difference of squares
(7x + 4)(7x + 4) is a Perfect square trinomial
(2x + 1)(x + 2) has Neither a difference of squares nor a perfect square trinomial.
(4x – 6)(x + 8) has Neither a difference of squares nor a perfect square trinomial.
(x – 9)(x – 9) is Perfect square trinomial
(–3x – 6)(–3x + 6) = Difference of squares.
Learn more about perfect square: