A reciprocal function, such as y = `frac(1)(x)`, creates two curves on the graph in opposite quadrants. There are values on the graph which cannot be found: x = 0 is a division by zero; and y = 0 requires x to be equal to infinity. The values of x = 0 and y = 0 (in this example) are known as the asymptotes: these are the lines that the curves tend towards, but never touch.
1. The function y = 3 + `frac(1)(x)` has been plotted on the graph below. What are the asymptotes for this graph?
Answer: x = 0 and y = 3
The value y = 3 requires x to be set to infinity. The value x = 0 is a division by zero.
2. Using the graph, above, estimate the value of y when x = -1.
Check the answer by substituting into the equation: y = 3 +`frac(1)(-1)` = 2.