What is a sign chart?

A sign chart is used in mathematics to analyze the signs of a function or expression in different intervals on the real number line. It is a way to visually represent the behavior of a function by dividing the domain into intervals and determining the sign of the function in each interval.

To create a sign chart, you start by identifying the critical points of the function, which are the points where the function changes sign. These critical points are typically the zeros of the function (where the function equals zero) or the points where the function is undefined.

Next, you pick test points within each interval between the critical points and evaluate the function at these test points to determine the sign of the function in that interval. You then plot the signs of the function in each interval on the number line to create the sign chart.

Sign charts are useful for determining the behavior of a function, such as finding the intervals where the function is positive, negative, increasing, or decreasing. They are also helpful in identifying the roots or zeros of a function, as they show where the function changes sign.