Lab05 GeoGebra and Function Graphs
1) Watch the review video.
2) Confirming functions and their inverses graphically
Select all check boxes and "Reflect f(x) ON/OFF"
a) Explore the applet sliders.
b) What can you conclude about and the inverse graph?
c) Change to , , and (pg 83 #7, 9, 11) and view all the inverse graphs.
3) Exploring Inverses by graphing and compositions
If two functions are inverses of each other, their graphs will be a reflection over the line y = x.
If you compose f(g(x)) or g(f(x)) the result will be x, which would overlap the graph of the line y = x.
a) Sketch and .
Use the applet to complete pg 83 Sect. 1.8 # 13, 15, 21. Sketch the graphs for your homework if you have not already done so.
4) Compositions and the Commutative Property
As stated in 3), f(g(x))=g(f(x)) for functions and their inverses because the inverse property applies to each pair of operations and the operations all cancel out, resulting in x.
a) Determine and algebraically (on paper) for and .
b) Use the applet above to graph f(x), g(x) and their compositions.
5) Math Modeling with Variations
6) Least Squares Regressions
From Algebra 1 and 2, we found curves of best fit. But how do you know if you have the BEST FIT?
a) Read http://www.mathwords.com/l/least_squares_regression_line.htm to learn about least squares regressions.
b) In the following applet, the blue points are data that has been collected. In an attempt to model the data using the best linear model, drag the red line of best fit until you find the least-squares regression line.
Sketch the graph yourself!
Which identity is best to use for this example?