The function f is defined by f(x)=-39^x The function g is a decreasing linear function. In the xy -plane, the graphs of y=f(x) and y=g(x) intersect at two points, (h,j) and (k,m) where jgt m When g(x)lt f(x) which of the following must also be true:

The correct answer is **h < k**.<br /><br />Here's why:<br /><br />* **Understanding the Functions:**<br /> * *f(x) = -39^x* is an exponential function that decreases rapidly as x increases.<br /> * *g(x)* is a decreasing linear function, meaning it has a constant negative slope.<br /><br />* **Intersection Points:** The graphs intersect at two points, indicating that there are two x-values where the output of *f(x)* and *g(x)* are equal. Since *j > m*, this means the point (h, j) is to the left of the point (k, m) on the x-axis.<br /><br />* **Inequality:** The inequality *g(x) < f(x)* means that the graph of *g(x)* is below the graph of *f(x)*. This occurs between the two intersection points.<br /><br />* **Conclusion:** Since the intersection points are ordered from left to right as (h, j) and (k, m), the region where *g(x) < f(x)* lies between these points. Therefore, **h < k**. <br />