Sketching Reciprocal Graphs (Edexcel IAL Maths)

Reciprocal Graphs - Sketching

Spec point — 1.11

Sketching reciprocal curves

What are reciprocal graphs?

• Reciprocal graphs involve equations with an $x$ term on the denominator e.g. $\frac{1}{x}$
• There are two basic reciprocal graphs to know for A level

$y=\frac{1}{x}$ and $y=\frac{1}{x^{2}}$

• 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

• All have two asymptotes

  • horizontal, y = 0 (x-axis)
  • vertical, x = 0 (y-axis)

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 dotted lines
• These graphs do not intercept either axis
• Graph transformations of them could cross the axes (see Translations)

Worked Example