Math Snap

STEP 1

1. We are dealing with an exponential function $f$ with base $b$.
2. The base $b$ must satisfy $b > 0$ and $b \neq 1$.
3. We need to determine the general form of the exponential function, its domain, and its range.

STEP 2

1. Identify the general form of the exponential function.
2. Determine the domain of the exponential function.
3. Determine the range of the exponential function.

STEP 3

The general form of an exponential function with base $b$ is:
$$f(x) = b^x$$

STEP 4

The domain of an exponential function is the set of all real numbers, because you can raise a positive number $b$ to any real power. In interval notation, this is:
$$(-\infty, \infty)$$

The range of an exponential function $f(x) = b^x$ where $b > 0$ and $b \neq 1$ is all positive real numbers. This is because $b^x$ is always positive for any real number $x$. In interval notation, this is:
$$(0, \infty)$$ The completed statement is:
The exponential function $f$ with base $b$ is defined by $f(x) = b^x$, $b > 0$ and $b \neq 1$. Using interval notation, the domain of this function is $(-\infty, \infty)$ and the range is $(0, \infty)$.