鶹Լ

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 \(y = 2^x\)

  • \(x = -2, y = 2^{-2} = 0.25\)
  • \(x = -1, y = 2^{-1} = 0.5\), etc.
\(\text{x}\)-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.