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Cubic, reciprocal and exponential graphs
You need to recognise the shapes of several standard graphs, and sketch them from their equations.
Cubic graphs
y = x3 has an S-shaped curve through the origin.
A cubic like y = x3 − 3x can have two turning points.
A cubic like y = x3 − 3x can have two turning points.
Reciprocal graphs
y = 1x has two separate curves and never touches the axes. The axes are asymptotes.
Exponential graphs
y = kx (k > 1) grows faster and faster. It passes through (0, 1) and never goes below the x-axis.
y = 2x: 1, 2, 4, 8, 16 for x = 0, 1, 2, 3, 4.
y = 2x: 1, 2, 4, 8, 16 for x = 0, 1, 2, 3, 4.
Find y when x = 5 for y = 3 × 2x.
- 25 = 32
- 3 × 32 = 96
Answer: 96
Know the shapes: linear, quadratic U, cubic S, reciprocal with asymptotes on the axes, exponential through (0, 1) rising steeply.
The interactive lesson includes the diagrams for this topic.
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