3-3 Transforming Linear Functions – We learned the transforming linear functions vocabulary: horizontal and vertical translation, stretches and compressions. We learned to graph transformations of linear functions by identifying the effect of replacing f(x) with kf(x), f(kx) for specific values of k. Next, we interpreted the key features of a graph of a linear function and use them to write the function that the graph represents. We learned to use mathematical modeling to represent a problem situation and to propose a solution. We tested and verified the appropriateness of math models.
Assignment: Complete the assigned problems for homework.
Today we continued working with absolute value functions. Ben has shown mastery in the ability to graph the function. We reviewed what makes the function stretch, shrink, and reflect. Then we considered the domain and range. Ben now knows the domain of abs. value functions is all real numbers. Next we determined the range is either all positive numbers or all negative numbers. I asked Ben how we can tell if the range would be positive or negative, and with some help, he was able to determine that if the leading term is positive, the range would be positive and if the leading term is negative the range would be negative.
Today's lesson took a bit for us to get started. Ben was not ready to work. He tried several different attempts to avoid working. We got through it and were able to be somewhat productive. We continued discussing Absolute Value Equations. We recalled the shape of the graph. Next we discussed how to make the graph compress, stretch, or reflect. We used the "I do - We do - You do" method of graphing equations. Then we discussed the domain and range. Ben was able to see that absolute value functions always have a domain of all real numbers, however the range will change depending on the transformation.
3-3 Transforming Linear Functions – We learned the transforming linear functions vocabulary: horizontal and vertical translation, stretches and compressions. We learned to graph transformations of linear functions by identifying the effect of replacing f(x) with f(x) + k, f (x + k) for specific values of k.
Assignment: Complete the assigned problems for homework.
Ben and I spoke about what happened today. He apologized to me. He said he doesn't know what it is, but he doesn't feel comfortable doing online schooling. Next time a teacher is sick, Virtual is not an option for him.
Today we continued working with the Absolute value function. We used a table to get the values and plotted them on the graph. We recalled the graph looks like a "V". Today we discussed what happens when a number is multiplied to the functions. We did several examples with 3, 1/2, and 4. Ben was able to determine if the number multiplied is greater than 1, it will stretch the graph vertically making the "V" taller/thinner. If the number multiplied was less than 1, it will shrink the graph vertically making the "V" shorter/wider.
Ben had a tough class today. He did not want to meet on Teams. I tried to get him to turn on his camera and he ignored me. After convincing him to turn it on, it was toward the ceiling. He hung up on me multiple times. I was disappointed with his lack of effort and how rude he was being to me. Administration had to facilitate him to get on multiple times. With 10 minutes left of class, he finally agreed to get online and showed only a sliver of his eyes. I was ok with that because he finally started to interact. We began discussing the Absolute Value function. We chose values for x to plug into the function and found the corresponding y values. Then we graphed the function and determined it was in the shape of a V.
3-2 Linear Functions – We reviewed the definition of a function. Then we practiced finding f(x) for various input values.
Assignment: Complete problems on writing a linear function rule from data in a table and finding the domain and range from a graph.
