To determine the cubic function that is obtained from the parent function, consider the transformations one at a time.
y=- (x-2)^3+1
Practice makes perfect
To determine the cubic function that is obtained from the parent function y=x^3 after the given sequence of transformations, let's consider the transformations one at a time.
Reflection Across the x-axis
We will start by reflecting the parent function across the x-axis by multiplying the whole function by - 1.
y=-(x)^3 ⇔ y=- x^3
Let's draw the graph of this function.
Vertical Translation 1 Unit Up
To perform a vertical translation 1 unit up, we need to add 1 to the whole function. The result is y=- x^3+1.
Horizontal Translation 2 Units Right
Finally, to perform a horizontal translation 2 units right, we need to subtract 2 from the x-variable, resulting in y=- (x-2)^3+1.
The cubic function that is obtained after the sequence of transformations is y=- ( x-2 )^3+1.
