Question

A parent function and transformed function are shown: Function

y=^3_/-x       y= -(0.4)^3_/-x-2

Which of the following describes the graph of the transformed function compared with the parent function? Select all that apply. reflected over the x-axis translated 2 units left translated 2 units right compressed by a factor of 0.4 stretched by a factor of 0.4 translated 2 units up translated 2 units down

Answer 1

Answer: A C D

Step-by-step explanation: hope this helps

Answer 2

Reflected over the x-axis

Translated 2 units right

Compressed by a factor of 0.4.

Explanation:

Given parent function :
`y=\sqrt[3]{-x}`

Transformed function :
`y=-0.4\sqrt[3]{-x-2}`.

According to rules of transformation y= -f(x) reflects f(x) over x-axis.

Therefore, first transformation is applied is
`y=-\sqrt[3]{-x}`, 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
`y=-4\sqrt[3]{-x}` 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
`y=-4\sqrt[3]{-x-2}` is translated 2 units right.

Therefore, the following rules being transformations are being applied in above given transformed function:

Reflected over the x-axis

Translated 2 units right

Compressed by a factor of 0.4.