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# Graphing and Shifting Logs

Lesson 2 of 11

## Objective: SWBAT graph a logarithmic function by reversing a table for it's inverse exponential function and stretch/shift these logarithmic functions.

## Big Idea: Shifty functions again... Now they are just logs! Students apply prior knowledge of parameter changes on functions to logs.

*50 minutes*

#### Warm-up

*5 min*

Students will review the definition of a logarithm by texting in their answers to the questions on pages 1-5 of the flipchart.

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**Environment:** Students should NOT have access to a graphing calculator for this lesson. By not allowing calculator use students are required to develop the graph of the logarithm function by using the inverse of the related exponential function. I will also be having my students work with their table mates on this worksheet to verify accuracy and help students who feel that they are having difficulties.

**Narrative:** In the graphing the log function worksheet, students will first explore how to graph the log function using an exponential function and their knowledge of inverses. I predict the graphing to go smoothly, but am guessing that my students will still be getting stuck on domain and range. For students still struggling on domain and range I will continue to emphasize the restrictions on domain and range. I plan to ask questions like:

- What values of x are allowed?
- Are any values of x not allowed?
- When I raise a number to a power, what kinds (positive, negative, decimal, whole, zero) of numbers do I get in return?
- What type of numbers can we never produce with exponents?

Next, students will extend their prior knowledge of shifting of functions to logarithmic graphs. Here, I will really encourage students to think about what they already know. I hope by this part in the year, this concept of how parameter changes affect basic functions should be pretty clear to students. Writing the transformation in words probably won’t be a problem, but students may struggle a bit more with the graphing. I am going to emphasize to students that these are *sketches* so they don’t need to be perfect. I am mostly interested in where the asymptote has shifted and the general shape of the graph.

Finally, students apply the definition of logarithms to solve very basic log equations. This is really just a preview so if students don’t reach this section it is ok.

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**Preparation:** For the closure part of today’s lesson students will need graph paper and a whiteboard or whiteboards with coordinate grids on them.

**Low Budget Tip:** If you want to make a really cheap, individual-sized graphing ‘whiteboard’ copy a coordinate grid to card stock and put the page in a page protector sleeve. Then, students can use whiteboard markers to write on the sleeve and it comes cleans up pretty easily. It doesn’t work as well as a real whiteboard, but I was able to make it with supplies at school and it works!

**Narrative: **Students will demonstrate their ability to master (or demonstrate their struggles with) today’s learning target by working through the 7 tasks on pages 6-7 of the flipchart. I will reveal one task at a time and having students hold up their solutions. I will encourage students to look at each other’s answers and will use a student’s board with a correct answer to show the class after every task.

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As homework tonight, I am going to ask that students complete their in-class activity from today. They will need to finish graphing and explaining the shifts in words.

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
- UNIT 8: Cyclical Patterns and Periodic Functions
- UNIT 9: Trigonometric Equations
- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: What Is A Log?
- LESSON 2: Graphing and Shifting Logs
- LESSON 3: Discovering Log Rules (because logs rule!)
- LESSON 4: Applying Log Rules
- LESSON 5: Puzzling Log Equations
- LESSON 6: Solving Exponential Equations Using Logs
- LESSON 7: Experts on Exponential Equations
- LESSON 8: Modeling Exponentials Using Logarithms
- LESSON 9: Speed Dating with Logarithms
- LESSON 10: Logarithmic Equations Test Review
- LESSON 11: Logarithmic Equations Unit Test