Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the form of an exponential function?

1. f(x) = ax + b

2. f(x) = b^n, where b > 0 and b ≠ 1

3. f(x) = log₀(x)

4. f(x) = √(x)

The correct answer is: f(x) = b^n, where b > 0 and b ≠ 1

The correct response highlights the general form of an exponential function, which is represented as \( f(x) = b^n \). In this context, \( b \) represents a positive constant base greater than zero, and it cannot be equal to one; this distinction is crucial because if \( b = 1 \), the function would not exhibit the characteristics typical of an exponential growth or decay. Exponential functions are defined by their constant rate of growth; as \( n \) increases, the value of \( f(x) \) increases exponentially, which is a key feature of these functions. For instance, if \( b = 2 \), as \( n \) takes on higher integer values, the outputs \( f(1), f(2), f(3) \) will be \( 2, 4, 8 \), respectively, demonstrating rapid growth. In contrast, the other options represent different types of functions. The first choice is a linear function, characterized by a constant additive relationship between \( x \) and \( f(x) \). The third choice describes a logarithmic function, which is the inverse of an exponential function. Lastly, the fourth option is a square root function, which expresses a relationship that increases