Question

The graph of the reciprocal parent function f(x)=1/x, is shifted 5 units up and 8 units to the left to create the graph of g(x). What function is g(x)?

A. g(x) = 1/(x+8) + 5
B. g(x) = 1/(x-5) + 8
C. g(x) = 1/(x-8) + 5
D. g(x) = 1/(x+5) + 8

Answer 1

The new function g(x) after shifting the reciprocal parent function f(x) = 1/x upwards by 5 units and left by 8 units is g(x) = 1/(x+8) + 5.

Step-by-step explanation:

The graph of the reciprocal parent function f(x) = 1/x is transformed into the function g(x) by shifting it 5 units up and 8 units to the left. The shift up corresponds to adding 5 to the function, which makes the outside part of the function + 5. The shift to the left corresponds to adding 8 inside the function's argument, changing x to (x + 8). Therefore, the new function g(x) is represented by g(x) = 1/(x+8) + 5.