The value of the a, h, and k are 2, 1, and 4 respectively after applying the transformation.
What is geometric transformation?
It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
After analyzing the function, we can perform the transformation:
We have a parent function:
[tex]\rm y = \sqrt[3]{x}[/tex]
First transformation:
Multiply by 2 functions will stretch by factor 2
[tex]\rm y = 2\sqrt[3]{x}[/tex]
Second transformation:
x → (x-1)
[tex]\rm y = 2\sqrt[3]{x-1}[/tex]
The function will shift right side by 1 unit.
Third transformation:
Add 4 to the function:
[tex]\rm y = 2\sqrt[3]{x-1}+4[/tex]
It will shift up by 4 units.
Compare with the function:
[tex]\rm y = a\sqrt[3]{x-h}+k[/tex]
a = 2, h = 1, and k = 4
Thus, the value of the a, h, and k are 2, 1, and 4 respectively after applying the transformation.
Learn more about the geometric transformation here:
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