AI generatedAlgebraGCSE Higher

Recognising and sketching an exponential graph

Interpret growth or decay from the base.

  • 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
An exponential with base greater than 1 grows. It has horizontal asymptote .
An exponential with base greater than 1 grows. It has horizontal asymptote .
Smooth curve; arrows show continuation.−3−2−1123−2−11234560
Smooth curve; arrows show continuation.

Example 2

Sketch the graph. State its key features.

Useful points
An exponential with base greater than 1 grows. It has horizontal asymptote .
An exponential with base greater than 1 grows. It has horizontal asymptote .
Smooth curve; arrows show continuation.−3−2−1123−22468100
Smooth curve; arrows show continuation.

Your turn

Question 1

Sketch the graph. State its key features.

Check answer
Useful points
An exponential with base greater than 1 grows. It has horizontal asymptote .
An exponential with base greater than 1 grows. It has horizontal asymptote .
Smooth curve; arrows show continuation.−3−2−11232.557.51012.51517.50
Smooth curve; arrows show continuation.
Question 2

Sketch the graph. State its key features.

Check answer
Useful points
An exponential with base greater than 1 grows. It has horizontal asymptote .
An exponential with base greater than 1 grows. It has horizontal asymptote .
Smooth curve; arrows show continuation.−3−2−1123−22468100
Smooth curve; arrows show continuation.
Question 3

Sketch the graph. State its key features.

Check answer
Useful points
An exponential with base greater than 1 grows. It has horizontal asymptote .
An exponential with base greater than 1 grows. It has horizontal asymptote .
Smooth curve; arrows show continuation.−3−2−112351015200
Smooth curve; arrows show continuation.
Question 4

Sketch the graph. State its key features.

Check answer
Useful points
An exponential with base greater than 1 grows. It has horizontal asymptote .
An exponential with base greater than 1 grows. It has horizontal asymptote .
Smooth curve; arrows show continuation.−3−2−1123510152025300
Smooth curve; arrows show continuation.
Question 5

Sketch the graph. State its key features.

Check answer
Useful points
An exponential with base greater than 1 grows. It has horizontal asymptote .
An exponential with base greater than 1 grows. It has horizontal asymptote .
Smooth curve; arrows show continuation.−3−2−1123−224681012140
Smooth curve; arrows show continuation.
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