Question

Rational Functions and Their Graphs 427 45-56, use transformations of f(x) = 1/x or f(x) = 1/x^2 to graph each rational function 46. g(x) = 1/x-2

Answer 1

To graph the rational function g(x) = 1/(x-2), start by considering the parent function f(x) = 1/x and applying transformations. Determine the vertical and horizontal asymptotes, and plot points using a table of values.

Step-by-step explanation:

To graph the rational function g(x) = 1/(x-2), we can start by considering the parent function f(x) = 1/x and applying transformations. Let's go step by step:

1. The function f(x) = 1/x has an asymptote at x = 0. However, for g(x) = 1/(x-2), the asymptote will shift 2 units to the right. So, the vertical asymptote of g(x) will be x = 2.

2. The function f(x) = 1/x has a horizontal asymptote at y = 0. The same will be true for g(x) = 1/(x-2). So, the horizontal asymptote of g(x) will be y = 0.

3. The graph of f(x) = 1/x is a decreasing function. The same will be true for g(x) = 1/(x-2), but it will be shifted 2 units to the right.

4. Finally, we can plot points on the graph of g(x) using a table of values, considering values of x and finding the corresponding values of y using the equation g(x) = 1/(x-2).

By following these transformations and plotting points, you can graph the rational function g(x) = 1/(x-2).