We will start by performing a vertical stretch on the parent function by a factor of 53. This is done by multiplying the parent function by 53. The resulting function is y= 53x^3.
Reflection Across the x-axis
Next, let's reflect the function across the x-axis by multiplying the whole function by - 1.
y=(- 1)(5/3x^3) ⇔ y=- 5/3x^3
Let's draw the graph of this function.
Vertical Translation 4 Units Down
To perform a vertical translation 4 units down, we need to subtract 4 from the whole function. The result is y=- 53x^3-4.
Horizontal Translation 3 Unit Right
Finally, to perform a horizontal translation 3 units right, we need to subtract 3 from the x-variable, resulting in y=- 53(x-3)^3-4.
The cubic function that is obtained after the sequence of transformations is y=- 53(x-3)^3-4.
