GCSE(F) GCSE(H)

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.

Answer: 2

Check the answer by substituting into the equation: *y* = 3 +`frac(1)(-1)` = 2.

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