Logarithmic Functions

I include Warm ups with a Rubric as part of my daily routine. My goal is to allow students to work on Math Practice 3 each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. The Video Narrative explains this lesson’s Warm Up- Logarithmic Functions which asks students to analyze a solved exponential equation.

I also use this time to correct and record the previous day's Homework.  

This lesson begins by relating a basic exponential zombie scenario to logarithms.   It is fundamental here and throughout the whole lesson to give students time to work with and talk about the mathematics going on.  Please see this video which talks about Classroom Discussions.  We look at the graphical, numerical and algebraic versions of these types of functions as inverses (Math Practice 7).  While I don't go into using composition of functions to prove inverses in Algebra 2, I do have students indentify it by switching the x and y variables and solving for the y.   

Please see the PowerPoint for detailed presentation notes.  

The next step is to identify the shape and major features of a basic logarithm function (Math Practice 7).  These are identified while looking at both the logarithmic function and its exponential inverse.  It is an interesting observation that both the intercept and the asymptote are inverses as well.  From here I ask the students to make a five point chart and graph another basic logarithm function.  Please see the PowerPoint for detailed presentation notes.  Finally, I ask the students to decide on two important points that we should use to make a sketch of logarithms. 

The final portion of this lesson relates the transformation of functions that the students have already done to logarithmic functions.  An important thing to note with these transformations, like radical functions, is that both vertical and horizontal reflections and dilations will affect these graphs.  Students already saw these with radical functions but some will probably struggle remembering whether a particular transformation is vertical or horizontal.  

The Homework is a combination of graphing practice as well as an extension to logarithmic functions whose base is 0<b<1.  

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.  

This Exit Ticket is a check whether the students can produce a logarithmic graph with both a horizontal and a vertical translation.