Question

Describe how z(x) is translated from the parent function f(x) z(x)=(2)/(x)-6 f(x)=(2)/(x)?

Answer 1

The function z(x) is a 6 unit downward translation of the parent function f(x). This is deduced from the '-6' in z(x), which implies the parent function has been shifted 6 units downwards.

Step-by-step explanation:

The question pertains to the concept of function transformations in mathematics, specifically

translations

. We are given two functions, the

parent function

, f(x)=(2)/(x), and a transformed version of it, z(x)=(2)/(x)-6. To describe how z(x) is a translation of the parent function, we need to understand how functions are translated. A function is translated vertically by adding or subtracting a constant after the function. Here, we see z(x) is f(x) subtracted by 6. This indicates that the parent function has been translated 6 units downward. In visual terms, every point on the graph of the parent function f(x) would be moved 6 units down to achieve the graph of z(x).

Learn more about Function Translations