Sketch the asymptotes and graph the function y equals start fraction 6 over left parenthesis x minus 2 right parenthesis end fraction plus 4.
The function is in the form y = 6/(x-2) + 4.
Asymptotes:
Vertical asymptote: x = 2 (x value that makes the denominator zero)
Horizontal asymptote: y = 4 (as x approaches positive or negative infinity, y approaches 4)
Graph:
The graph of the function will approach the vertical asymptote x = 2 as x gets closer to 2 and approach the horizontal asymptote y = 4 as x approaches positive or negative infinity. The graph will have a vertical stretch by a factor of 6 and a vertical shift up by 4 units. It will have a shape similar to a hyperbola.
(Note: The graph cannot be drawn here due to limitations of text based response.)