Question

The graph of the reciprocal parent function, f(x) = is shifted 8 units down and 6 units to the left to create the graph of g(x). What function is g(x)?

Answer 1

Answer:

C.

Explanation:

The reciprocal parent function is:

f(x) = 1/x

If a function h(x) = f(x) - c, we can say that h(x) is f(x) shifted c units down. Additionally, if a function f(x) = f(x+c), we can say that h(x) is f(x) shifted c units to the left.

Therefore, the function g(x) that is equal to f(x) but shifted 8 units down and 6 unit to the left is:

$\begin{gathered} g(x)=f(x+6)-8 \\ g(x)=\frac{1}{x+6}-8 \end{gathered}$

Therefore, the answer is C.