Question

Graph f(x) = 1/x after it has been translated 2 units right and 6 units down.

a) What are its asymptotes?
b) Write down the equation of the translated graph.

A. a) Vertical asymptote at x = -2, horizontal asymptote at y = -6
b) f(x) = 1/(x + 2) - 6

B. a) Vertical asymptote at x = 2, horizontal asymptote at y = -6
b) f(x) = 1/(x - 2) - 6

C. a) Vertical asymptote at x = 6, horizontal asymptote at y = -2
b) f(x) = 1/(x - 6) - 2

D. a) Vertical asymptote at x = -6, horizontal asymptote at y = 2
b) f(x) = 1/(x + 6) + 2

Answer 1

To graph f(x) = 1/x after it has been translated 2 units right and 6 units down, replace x with (x - 2) and subtract 6 from the equation.

Step-by-step explanation:

To graph the function f(x) = 1/x after it has been translated 2 units right and 6 units down:

1. Start with the graph of y = 1/x. Notice that this function has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.
2. To translate the graph 2 units right, replace x with (x - 2) in the equation. This will shift the entire graph 2 units to the right.
3. To translate the graph 6 units down, subtract 6 from the equation. This will shift the entire graph 6 units down.

The resulting equation of the translated graph is f(x) = 1/(x + 2) - 6.

The asymptotes for the translated graph are a vertical asymptote at x = -2 and a horizontal asymptote at y = -6.