# Tech Time

## Objective

SWBAT evaluate the effect on a graph of replacing f(x), by f(x)+k, k f(x), f(kx), and f(x+k) for specific values of k using technology. SWBAT explain the effects described above using technology.

#### Big Idea

Use graphing calculators as tools to evaluate and explain, yes, explain!, changes to a graph.

## Set the Stage

10 minutes

Your students will need graphing calculators for this lesson - I have a set of TI 84s we use.  I begin with this challenge question on the board, "What does the graph of f(x) = 2^x look like?"  Most of my students will ask if they can use a graphing calculator to answer this and I tell them they can use whatever tools they want as long as they can identify key points to the graph and explain what they represent. (MP2, MP5)  After a minute or two I ask for volunteers to identify key points and explain the graph. Acceptable responses would include saying that the graph curves up to the right, crosses the y-axis at (0, 1) and has a horizontal asymptote at x = 0.  In addition I expect some comment about the f(x) values all being 2 to some power because that's what the original function is.  It's surprising the number of students who haven't really made the connection between the function and the actual pairs of points on the graph, so I make sure to emphasize this aspect of what they're seeing.

The next challenge is for my students to use their calculator to try to duplicate a graph projected on the board of the same parent function [but they don't know that yet - simply translated].  For example I might use f(x)= 2^x - 3 making sure to label the y-intercept (0, -2) as well as a few additional points like (1, -1), (2, 1) and (3, 5). (MP4) I randomly select three or four students [because that's how many fit well] to post the equation they found on the board then have the class try these in their calculators to see which, if any, fit the challenge graph until we find one that works. (MP1) To conclude this activity I remind them of previous lessons where we've looked at transformations of functions and how those are reflected in the graphs, then ask what the parent function and transformation were for this problem.

## Put It Into Action

35 minutes

*Common Core includes K-12 ELA Speaking and Listening Standards

## Wrap It Up

5 minutes

To wrap up this lesson I ask my students to pair-share what they think about using graphing calculators with a focus on when they are helpful and when they aren't. (MP5) I then ask each student to write a brief compare/contrast piece about when to use graphing calculators and when other tools or strategies are more appropriate and why.  I tell them they can use examples but need to write out their ideas and explanations in complete sentences.  If you want a more focused ticket-out-the-door you might have them respond to some specific questions like: