Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent.

Front

How can you identify an exponential function from a table of values?

Back

An exponential function can be identified by a constant ratio of the differences between consecutive y-values when the x-values are equally spaced.

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases multiplicatively.

Front

What does the base of an exponential function represent?

Back

The base of an exponential function indicates the growth (if greater than 1) or decay (if between 0 and 1) rate of the function.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a * b^x, where a is the initial value and b is the growth factor.

Front

Can an exponential function ever be negative?

Back

No, an exponential function is always positive for real numbers when a > 0 and b > 0.

Front

What is the domain and range of an exponential function?

Back

The domain of an exponential function is all real numbers, while the range is all positive real numbers.

Front

What is the significance of the y-intercept in an exponential function?

Back

The y-intercept of an exponential function is the value of the function when x = 0, which is equal to the constant a.

Front

How do you determine if a function is exponential from a graph?

Back

A function is exponential if its graph shows a rapid increase or decrease, forming a curve that is not a straight line.

Front

What is the effect of changing the base of an exponential function?

Back

Changing the base affects the rate of growth or decay; a larger base results in faster growth, while a base less than 1 results in decay.