A manufacturer's cost is given by $C = 500 \sqrt [ 3 ] { n } + 512$, where $C$ is the cost and $n$ is the number of parts produced. Describe the transformations needed to obtain the graph of this function from the graph of $y = \sqrt { n }$.
A) Stretch vertically by a factor of 500 and shift up 512 units.
B) Stretch vertically by a factor of 500 and shift 512 units to the left.
C) Stretch vertically by a factor of 500 and shift 512 units to the right.
D) Shift 500 units to the left and shift up 512 units.

Question

Quizplus · Accepted Answer

The given function $C = 500 \sqrt [ 3 ] { n } + 512$ involves a cube root transformation ($\sqrt[3]{n}$) rather than a square root ($\sqrt{n}$), indicating a vertical stretch by a factor of 500 and an upward shift of 512 units from the basic cube root graph, not the square root graph as mentioned in the question. However, understanding the intent behind the question and the options provided, option A correctly describes the transformations in terms of vertical stretch and upward shift, despite the discrepancy in root type.

A Manufacturer's Cost Is Given By C=500n3+512C = 500 \sqrt [ 3 ] { n } + 512C=5003n​+512

A Manufacturer's Cost Is Given By $C = 500 \sqrt [ 3 ] { n } + 512$