Questiononential Functions Question 1, 4.1.C1 HW Score: 0\%, 0 of 21 points Points: 0 of 1
Select the answers that best complete the given statement.
The exponential function $f$ with base $b$ is defined by $f(x)=$ $\square$ , $b>0$ and $b \neq 1$ . Using interval notation, the domain of this function is $\square$ and the range is $\square$ $\square$ .

Studdy Solution

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:
$(-\infty, \infty)$

STEP 5

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 $(0, \infty)$ .

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