Questions: Is the following an exponential function? y=3^2

Transcript text: Is the following an exponential function? \[ y=3^{2} \]

Solution

Solution Steps

To determine if \( y = 3^2 \) is an exponential function, we need to understand the definition of an exponential function. An exponential function is typically in the form \( y = a^x \), where \( a \) is a constant and \( x \) is a variable. In this case, \( y = 3^2 \) is a constant value, not a function of a variable \( x \). Therefore, it is not an exponential function.

Step 1: Understanding the Definition of Exponential Functions

An exponential function is defined as a function of the form \( y = a^x \), where \( a \) is a constant and \( x \) is a variable. This means that the output \( y \) depends on the variable \( x \).

Step 2: Analyzing the Given Expression

The expression given is \( y = 3^2 \). Here, \( 3^2 \) evaluates to \( 9 \), which is a constant value. Since there is no variable \( x \) present in the expression, it does not fit the definition of an exponential function.

Step 3: Conclusion

Since \( y = 3^2 \) does not involve a variable and is simply a constant, it is not classified as an exponential function.