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

which of the following describes the graph of ( y=sqrt3{8 x - 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{8 x - 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)}=2\sqrt[3]{x - 8}) (because (\sqrt[3]{8}=2)).

Step2: Analyze the transformation

For a cube - root function (y = a\sqrt[3]{x - h}+k) compared to the parent function (y=\sqrt[3]{x}):

  • The factor (a) represents a vertical stretch or compression. Here (a = 2), so there is a vertical stretch by a factor of (2).
  • The value of (h): For the function (y = 2\sqrt[3]{x - 8}-5), when (h>0), the graph of the parent function (y=\sqrt[3]{x}) is translated (h) units to the right. Here (h = 8), so it is translated (8) units to the right.
  • The value of (k): For the function (y=2\sqrt[3]{x - 8}-5), when (k<0), the graph of the parent function (y = \sqrt[3]{x}) is translated (|k|) units down. Here (k=-5), so it is translated (5) units down.

Answer:

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