Exponential Function Text
Definition of Exponential Function
$$f(x) = a^x \quad (a > 0 \land a \neq 1)$$
If a=1, 1 raised to the power of x is always 1, this function looks like this, not very meaningful, so not studied
If a=0, 0 raised to the power of x is currently considered to be 0, not very meaningful, so not studied
If a<1, x raised to a negative number is more complex, to be studied later
Graph of Exponential Function
Domain: x \in \mathbb{R}
Range: (0, +\infty)
Monotonicity: When a > 1, the function is increasing; when 0 < a < 1, the function is decreasing
Asymptote: x-axis
Fixed point: (0, 1)
Symmetry: y = a^x and y = \left(\frac{1}{a}\right)^x are symmetric about the y-axis