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Other graphs - OCRExponential graphs (Higher)

The most commonly occurring graphs are quadratic, cubic, reciprocal, exponential and circle graphs. Their equations can be used to plot their shape.

Part ofMathsAlgebra

Exponential graphs (Higher)

Exponential graphs are graphs in the form \(y = k^x\). These graphs increase rapidly in the \(y\) direction and will never fall below the \(x\)-axis.

An exponential graph will look like this:

Exponential graph showing y = k to the power of x

Example

Let's look at \(y = 2^x\)

  • when \(x = -2, y = 2^{-2} = 0.25\)
  • when \(x = -1, y = 2^{-1} = 0.5\)
\(\text{x}\)-2-1012345
\(\text{y = 2}^x\)0.250.512481632
\(\text{x}\)
-2
-1
0
1
2
3
4
5
\(\text{y = 2}^x\)
0.25
0.5
1
2
4
8
16
32

Plotting these points, we can see the steep increase in the graph in the \(y\) direction.

A line graph with a curve from x-2, y0 to x5, y32.
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The equation of a circle – Higher
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Reciprocal graphs

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