A different mathematical graphic program will be used in this activity. When students try to solve a function such as y=x+1-logx they have a limitation from Algebra Xpressor. Let us think about the function y=x+1-logx. In a traditional way of graphing, I used to draw the function combining two graphs as y=x+1, and y=-logx since I could figure out how the two graphs are very easily. In today's lesson, students will use the concept of derivative and its interpretation. First, think about the differentiated function of y=x+1-logx. It will be y=(x-1)/x. The differentiated function is easy enough to draw with pencil and paper. The next is the graph of it.

It says the graph of y=x+1-logx will have tangent lines with positive slopes at each point of y=x+1-logx when values of x are greater than 1. While values of x are between 0 and 1, the graph will have negative- slope tangent lines at each point of y=x+1-logx. A point (1,2) will be on the graph, and y-values will increase continuously. The graph of y=x+1-logx is following. Students should be careful in understanding the scales of x and y-axis.

The domain of the function was restricted to all positive numbers since logx doesn't have value for negative x values.