STRETCH Optional 1 Describe how you can tell from an equation whether a function increases, decreases, or is constant.

One common way to tell if a function is increasing, decreasing, or constant is to examine its rate of change. Here’s how you can do that: 1. Look at the derivative if you’re working with calculus. For a function f(x), compute f ′(x):  • If f ′(x) > 0 for every x in the domain, then f(x) is increasing.  • If f ′(x) < 0 for every x in the domain, then f(x) is decreasing.  • If f ′(x) = 0 for every x in the domain, then f(x) is constant.  This is because the derivative tells you the slope or the instantaneous rate of change of the function at any given point. 2. For a linear function of the form f(x) = mx + b:  • If m > 0, the function is increasing.  • If m < 0, the function is decreasing.  • If m = 0, the function is constant.  This works because the coefficient m gives the slope of the line. 3. Alternatively, if you do not want to use calculus, you can pick two arbitrary points, a and b, with a < b, and examine the difference f(b) – f(a):  • If f(b) – f(a) is positive for every such pair, the function is increasing.  • If f(b) – f(a) is negative for every such pair, the function is decreasing.  • If f(b) – f(a) equals zero for every such pair, the function is constant. Each of these approaches leverages information from the equation that describes how the function behaves as x changes.