Guided Explore-Graphing
1) Predict: What do you think the graph of \(f\left(x\right)=\left|x\right|+\left|x-3\right|\) would look like? Explain your reasoning.
2) Explore: Turn on the different functions in the Desmos app below. Make three observations about functions with multiple absolute value quantities.
1) Predict: What do you think the graph of \(f\left(x\right)=\left|x\right|+\left|x-3\right|\) would look like? Explain your reasoning.
2) Explore: Turn on the different functions in the Desmos app below. Make three observations about functions with multiple absolute value quantities.
3) Apply: In the previous question, you explored functions with multiple turning points. Can you figure out where those turning points would be by just looking at a function, without seeing it's graph? Identify the turning points in each of the following problems.
a) \(f\left(x\right)=\left|x\right|+\left|x+6\right|\)
b) \(f\left(x\right)=\left|x\right|+\left|6-2x\right|\)
c) \(f\left(x\right)=\left|x-3\right|+\left|6-4x\right|+3x\)
Check your answers by plugging the equations into Desmos above. To type absolute value into Desmos, you can either use the vertical bar on your keyboard, or type abs( followed by the quantity inside the absolute value and then close parenthesis.
4) Extend: Can you write absolute value functions given the following conditions? Note, these are open-ended problems with many answers.
a) Write a function with turning points where \(x = 0\) and \(x = 4\).
b) Write a function whose graph has three increasing pieces and no decreasing pieces.
c) Write a function whose graph has turning points where \(x = -2\) and \(x = 3\) and there is at least one horizontal piece.
Check your answers by plugging the equations into Desmos above.
Guided Explore-Solving
Complete the Desmos activity below by joining or typing in the class code provided by your teacher.