What are reciprocal graphs?
- Reciprocal graphs involve equations with an term on the denominator e.g.
- There are two basic reciprocal graphs to know for A level
- The second one of these is always positive
More reciprocal graphs
- You also need to recognise graphs where the numerator is not one
- The sign of a shows which part of the graph the curves are located
- The size of a shows how steep the curves are
- The closer a is to 0 the more L-shaped the curves are
- horizontal, y = 0 (x-axis)
- vertical, x = 0 (y-axis)All have two asymptotes
How do I sketch a reciprocal graph?
STEP 1 Use the sign of “a” to locate the curves
and use the size of “a” to gauge the steepness of the curve
STEP 2 Sketch the graph
STEP 3 Label the points x = 1 and x = -1 as a guide to the scale of your graph
STEP 4 Draw asymptotes with a dotted line Draw asymptotes with dotted lines
- These graphs do not intercept either axis
- Graph transformations of them could cross the axes (see Translations)