which of the following describes the graph of $y = sqrt3{8x - 64}-5$ compared to the parent cube root…

which of the following describes the graph of $y = sqrt3{8x - 64}-5$ compared to the parent cube root function?\nstretched by a factor of 2 and translated 64 units right and 5 units down\nstretched by a factor of 8 and translated 8 units right and 5 units down\nstretched by a factor of 2 and translated 8 units right and 5 units down\nstretched by a factor of 8 and translated 64 units right and 5 units down

which of the following describes the graph of $y = sqrt3{8x - 64}-5$ compared to the parent cube root function?\nstretched by a factor of 2 and translated 64 units right and 5 units down\nstretched by a factor of 8 and translated 8 units right and 5 units down\nstretched by a factor of 2 and translated 8 units right and 5 units down\nstretched by a factor of 8 and translated 64 units right and 5 units down

Answer

Explanation:

Step1: Rewrite the function

Rewrite $y = \sqrt[3]{8x - 64}-5$ as $y=\sqrt[3]{8(x - 8)}-5$. Since $\sqrt[3]{8(x - 8)}=\sqrt[3]{8}\cdot\sqrt[3]{x - 8}=2\sqrt[3]{x - 8}$, the function is $y = 2\sqrt[3]{x - 8}-5$.

Step2: Analyze the transformation

For the cube - root parent function $y=\sqrt[3]{x}$, the coefficient 2 in front of $\sqrt[3]{x - 8}$ represents a vertical stretch by a factor of 2. The $x-8$ inside the cube - root function represents a horizontal translation 8 units to the right. The $- 5$ outside the cube - root function represents a vertical translation 5 units down.

Answer:

stretched by a factor of 2 and translated 8 units right and 5 units down