3.1 Exponential Functions

Notes

An exponential function has the form $f(x) = a \cdot b^x$ with $b > 0$ and $b \ne 1$.

• If $b > 1$ it shows growth; if $0 < b < 1$ it shows decay.
• The y-intercept is $a$. The graph has a horizontal asymptote, $y = 0$ for the basic form.
• $f(x) = b^x + k$ has horizontal asymptote $y = k$.
• Domain: all real numbers. Range of $2^x$: $(0, \infty)$.
• Example: $f(x) = 2^x$ gives $f(3) = 8$ and $\displaystyle f(-2) = \frac{1}{4}$.