AI generatedAlgebraKS3 / GCSE

Recognising and sketching a reciprocal graph

Recognising and sketching a reciprocal graph.

  • Check axis labels and scales before reading values.
  • Use key points and the correct curve shape. Join a curved graph smoothly.
  • An asymptote is approached; do not join separate branches across it.

Example 1

Sketch the graph. State its key features.

Useful points
is excluded. The axes are asymptotes: the curve approaches them without meeting them.
is excluded. The axes are asymptotes: the curve approaches them without meeting them.
Smooth curve; arrows show continuation.−8−6−4−22468−8−6−4−224680
Smooth curve; arrows show continuation.

Example 2

Sketch the graph. State its key features.

Useful points
is excluded. The axes are asymptotes: the curve approaches them without meeting them.
is excluded. The axes are asymptotes: the curve approaches them without meeting them.
Smooth curve; arrows show continuation.−8−6−4−22468−8−6−4−224680
Smooth curve; arrows show continuation.

Your turn

Question 1

Sketch the graph. State its key features.

Check answer
Useful points
is excluded. The axes are asymptotes: the curve approaches them without meeting them.
is excluded. The axes are asymptotes: the curve approaches them without meeting them.
Smooth curve; arrows show continuation.−8−6−4−22468−8−6−4−224680
Smooth curve; arrows show continuation.
Question 2

Sketch the graph. State its key features.

Check answer
Useful points
is excluded. The axes are asymptotes: the curve approaches them without meeting them.
is excluded. The axes are asymptotes: the curve approaches them without meeting them.
Smooth curve; arrows show continuation.−8−6−4−22468−8−6−4−224680
Smooth curve; arrows show continuation.
Question 3

Sketch the graph. State its key features.

Check answer
Useful points
is excluded. The axes are asymptotes: the curve approaches them without meeting them.
is excluded. The axes are asymptotes: the curve approaches them without meeting them.
Smooth curve; arrows show continuation.−8−6−4−22468−8−6−4−224680
Smooth curve; arrows show continuation.
Question 4

Sketch the graph. State its key features.

Check answer
Useful points
is excluded. The axes are asymptotes: the curve approaches them without meeting them.
is excluded. The axes are asymptotes: the curve approaches them without meeting them.
Smooth curve; arrows show continuation.−8−6−4−22468−8−6−4−224680
Smooth curve; arrows show continuation.
Question 5

Sketch the graph. State its key features.

Check answer
Useful points
is excluded. The axes are asymptotes: the curve approaches them without meeting them.
is excluded. The axes are asymptotes: the curve approaches them without meeting them.
Smooth curve; arrows show continuation.−8−6−4−22468−8−6−4−224680
Smooth curve; arrows show continuation.
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