Final answer:
To graph the function f(x) = (x - 2) / (x - 1), identify the vertical asymptote at x = 1, the horizontal asymptote at y = 1, and the vertical intercept at (0, -2). The graph will approach but not touch the vertical asymptote and will approach the horizontal asymptote as x increases or decreases.
Step-by-step explanation:
To graph the rational function f(x) = (x - 2) / (x - 1), we need to consider several features of this function:
- The vertical asymptote is at x = 1, because the denominator is zero at this point.
- The horizontal asymptote of the function is y = 1, since the degrees of both numerator and denominator are equal, and the ratio of their leading coefficients is 1.
- There is no horizontal intercept as the numerator is never zero for any value of x.
- The vertical intercept is at (0,-2), found by setting x to 0 in the function
The graph should be drawn with careful attention to these points, making sure to include the asymptotes and intercepts accurately. The function will approach but not touch the vertical asymptote, and as x becomes very large or very small, the function will approach the horizontal asymptote.