Exponential Functions

Revision of exponents

An exponent indicates the number of times a certain number (the base) is multiplied by itself. The exponent, also called the index or power, indicates the number of times the multiplication is repeated. For example, \(\text{10}^{3} = 10 \times 10 \times 10 = \text{1 000}\).

Graphs of the exponential function \(f(x) = b^{x}\)

The value of \(b\) affects the direction of the graph:

• If \(b > 1\), \(f(x)\) is an increasing function.
• If \(0 < b < 1\), \(f(x)\) is a decreasing function.
• If \(b \leq 0\), \(f(x)\) is not defined.

\(y = b^{x}\)	\(b > 1\)	\(0 < b < 1\)	\(b \leq 0\)
			Not defined