While using a table of values to estimate the value of \( x \) where \( f(x)=g(x) \), you see that there are three sign changes in the \( f(x)-g(x) \) column. How many possible solutions for \( x \) are there? If there are three sign changes in the \( f(x)-g(x) \) column, there will be \( \square \) possible solutions Points possible: 1 Allowed attompte: 2 Check Answer

If there are three sign changes in the \( f(x)-g(x) \) column, there will be \( 3 \) possible solutions. Each sign change indicates a crossing of the x-axis, which corresponds to a solution where \( f(x) = g(x) \). Looking at the behavior of continuous functions, the Intermediate Value Theorem reinforces this idea. It tells us that if a continuous function takes on opposite signs at two points, then there must be at least one value in between where the function equals zero. Therefore, with each sign change observed for \( f(x)-g(x) \), we can confidently claim a corresponding solution exists between those intervals.