Student Problem #4: Unit I Concept 2

• What is this about?

This picture shows a problem from Unit I Concept 2 which is graphing logarithmic functions and identifying x-intercepts, y-intercepts, asymptote, domain, and range (4 points on graph minimum). We will review this concept by using the given function and find all the pieces for the graph to make it more accurate. The logarithmic function is different with exponential function because its form is log base b (x-h) + k. Unlike the exponential function, the asymptote of logarithmic function is x=h. There will be no restriction for the range because it is a vertical asymptote; however, the domain has its restriction that bases on the asymptote. This type of graph is similar with the exponential graph when it comes to set up the equation to find x- and y-intercepts. 

•  What does the reader need to pay attention to?

The reader should to pay attention when they solve for x- and y-intercept. There will some problems that have no x- and -y-intercepts. We can guess right away that there is no y-intercept if the asymptote is greater than 0 and the graph will stay on the right side of the asymptote. Remember that the graph can NEVER EVER cross the vertical asymptote. To be able to solve for x- and y-intercepts, we need to review some rules for log. We CANNOT LOG a NEGATIVE number which means it is undefined. To find x-intercept, we should know the word EXPONENTIATE because we will exponentiate both sides to get rid of the log and then solve for x.