Which of the following describes the graph of y-3/8x-64-5 compared to the parent cube root function?
stretched by a factor of 2 and translated 64 units right and 5 units down
stretched by a factor of 8 and translated 8 units right and 5 units down
stretched by a factor of 2 and translated 8 units right and 5 units down
stretched by a factor of 8 and translated 64 units right and 5 units down

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

Step-by-step explanation:

A general form of a cube root function has four parameters: a, b, c, and d:

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

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.

problem:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

f(5/2) = 10/3

i hope this !