Answer:
Stretched by a factor of 2 and translated 8 units right and 5 units down
Step-by-step explanation:
[tex]y = \sqrt [3]{8x - 64} - 5 = \sqrt [3]{8(x - 8)} - 5[/tex]
A general form of a cube root function has four parameters: a, b, c, and d:
[tex]y = a\sqrt[3]{b(x - c)} + d[/tex]
The effects of each parameter are
a — stretches in the y direction by a factor of a
b — stretches in the y direction by a factor of ∛b
c — translates c units in x direction
d — translates d units in y direction
In your function, a = 1, b = 8, c = 8, and d = -5, so it is
- stretched vertically by a factor of 2
- translated 8 units to the right
- translated 5 units down
The diagram below shows you function (purple graph) and the parent cube root function (blue). The parent function is translated eight units to the right and five units own (red arrows).The blue arrows show that the function is stretched vertically by a factor of two.
