TASC Math Exam: Working with Exponential Functions

By Stuart Donnelly

You will probably encounter questions on the TASC Math exam that involve exponential functions. If the problems appear in the form of a graph or a table, the following instructions will help you navigate through them.

An exponential function is when the independent variable is in the exponent of a constant. The base of the function must be greater than 0 and not equal to 1. Some examples of exponential functions are:


General shape of an exponential function for a > 1.

If the base of the exponential function is a fraction, then the graph falls rapidly to the right, as shown here.

General shape of an exponential function for 0 < a < 1.

Looking for these general shapes when given a graph will indicate whether the graph represents an exponential function.

If you’re given a table, to determine whether the function is exponential, check if there’s a common multiple difference, meaning you can multiply each of the y-values by a number to get to the next y-value. This indicates that the function is exponential and, in fact, that that number is your base.

To write an equation for an exponential function, follow these steps:

  1. Find the common multiple difference (this is your base, b).
  2. Find your y-intercept—this is the coefficient of your exponential function (a).
  3. Substitute your values for a and b into the general form of an exponential:


For example:


First find whether there’s a common multiple difference. It’s important to note that the x-values are evenly spaced, which allows the common multiple to be identifiable.


You now know that your base is 2. Looking for your y-intercept, you see it’s (0, 3), so a = 3. Now substitute these values into