Question

in 1-2 sentences describe the difference between the graphs of f(x) = 1/(x - 2) + 3 the parent function f(x) = 1/x

Answer 1

The graph of \( f(x) = \frac{1}{x - 2} + 3 \) is a transformation of the parent function \( f(x) = \frac{1}{x} \) that is shifted 2 units to the right and 3 units up, resulting in a new vertical asymptote at \( x = 2 \) and a horizontal asymptote at \( y = 3 \). In contrast, the parent function has vertical and horizontal asymptotes at \( x = 0 \) and \( y = 0 \), respectively.