## Classroom Discussions - Section 2: Introduction to Logarithmic Functions

# Logarithmic Functions

Lesson 9 of 15

## Objective: Students will be able to graph logarithmic functions.

*101 minutes*

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.

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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.

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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.

#### Resources

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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.

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#### Exit Ticket

*5 min*

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.

#### Resources

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- UNIT 1: Modeling with Expressions and Equations
- UNIT 2: Modeling with Functions
- UNIT 3: Polynomials
- UNIT 4: Complex Numbers and Quadratic Equations
- UNIT 5: Radical Functions and Equations
- UNIT 6: Polynomial Functions
- UNIT 7: Rational Functions
- UNIT 8: Exponential and Logarithmic Functions
- UNIT 9: Trigonometric Functions
- UNIT 10: Modeling Data with Statistics and Probability
- UNIT 11: Semester 1 Review
- UNIT 12: Semester 2 Review

- LESSON 1: Rational Exponents
- LESSON 2: Real Number Exponents
- LESSON 3: Exponential Models Day 1 of 2
- LESSON 4: Exponential Models Day 2 of 2
- LESSON 5: Exponential Functions
- LESSON 6: Exponential Decay Functions
- LESSON 7: Simplifying Logarithms
- LESSON 8: Exponential and Logarithmic Equations
- LESSON 9: Logarithmic Functions
- LESSON 10: Exponential Growth and Interest Day 1 of 2
- LESSON 11: Exponential Growth and Interest Day 2 of 2
- LESSON 12: Natural Logarithms
- LESSON 13: Exponential and Logarithmic Functions Review Day 1
- LESSON 14: Exponential and Logarithmic Functions Review Day 2
- LESSON 15: Exponential and Logarithmic Functions Test