Read the problem carefully. Identify which function is being tested and which function is known. Look for the question in the problem, such as "Can we accept the model f(x) = x^2 + 3x knowing that f(x) > x+2?"
Draw the known function on a piece of graph paper. Solve the function for several values of x. Plot the resulting f(x) value for each value of x. Sketch a line through all the points. Shade the area above the line if the function is a "greater-than" inequality (f(x) >) or shade the area below the line if the function is a "less-than" inequality (f(x) <).
Follow the process from above to plot several points of the function being tested. Draw a line through the points. Shade as described above if the function is an inequality.
Check whether all points of the function being tested exist within the area described by the known function. For example, the function f(x) > x+2 describes all the area above a line that starts at y = 2 and has a slope of 1. The hypothetical function f(x) = x^2 +3x describes all the points on a line that starts at y = 0 and increases exponentially. The hypothetical function is outside of the area of the known function when x = 0.
Accept the function if it lies within the area of the known function. Reject the function if it exists outside of the area of the known function at any point. In the example, we reject the hypothetical function because it is less than the known function at x = 0.