To determine whether the given function \( y = 6^x \) is an exponential function, we should first understand the defining characteristics of an exponential function.
An exponential function is a mathematical expression in the form:
[tex]\[
y = a^x
\][/tex]
where:
- \( a \) is a positive constant (base),
- \( x \) is the exponent and can be any real number,
- \( y \) is the output of the function.
Key features of exponential functions include:
1. The variable \( x \) is located in the exponent.
2. The base \( a \) is a positive constant.
Consider our given function:
[tex]\[
y = 6^x
\][/tex]
Step-by-Step Verification:
1. Check the Form:
- The given function is expressed as \( y = 6^x \), which matches the general form \( y = a^x \).
2. Identify the Base:
- Here, the base \( a \) is 6, which is a positive constant (base \( a > 0 \)).
3. Check the Exponent:
- The variable \( x \) is indeed in the exponent.
Given these observations, the function \( y = 6^x \) fulfills the criteria for being an exponential function:
- The format \( y = a^x \) is met with \( a = 6 \) and \( x \) in the exponent.
- The base \( a = 6 \) is a positive constant.
Therefore, the function \( y = 6^x \) is an exponential function.
In summary, the correct answer is:
[tex]\[
\text{exponential}
\][/tex]
