Respuesta :
Answer:
Reflected over the x-axis
Translated 2 units right
Compressed by a factor of 0.4.
Step-by-step explanation:
Given parent function :[tex]y=\sqrt[3]{-x}[/tex]
Transformed function : [tex]y=-0.4\sqrt[3]{-x-2}[/tex].
According to rules of transformation y= -f(x) reflects f(x) over x-axis.
Therefore, first transformation is applied is [tex]y=-\sqrt[3]{-x}[/tex], reflects f(x) over x-axis.
Second we have 0.4 in front of cube root.
According to rules of transformation, for y = k f(x), if k is less than 1, it would compressed by a factor k.
Therefore, second transformation is applied is [tex]y=-4\sqrt[3]{-x}[/tex] compressed by a factor 0.4.
Now, third thing we can see that -x is being subtracted by -2.
According to rules of transformation, for y=f(x-c) it would be a horizontal translation of c unit to the right.
Therefore, fourth transformation is applied is [tex]y=-4\sqrt[3]{-x-2}[/tex] is translated 2 units right.
Therefore, the following rules being transformations are being applied in above given transformed function:
