If necessary review the first DERIVE assignment to make sure you know how to write and solve equations, graph formulas and functions, and perform other basic operations.
Authoring Functions and Using the Vector Command:
Author the line f(x) = 2 x^2 + 3
Author the line f(x) := 2 x^2 + 3
Which line appears to define x as a function? Do you understand why the : is necessary in front of the equal sign?
Mentally calculate f(2). Then author the expression f(2) and choose Simplify > Basic. Your result should reconcile with your mental calculation.
Highlight the expression f(2) once more and choose Simplify > Approximate and get your result. This result should reconcile with your previous results.
Repeat the preceding two steps, but omit the mental calculations, for f(2.738). Does Simplify > Basic or Simplify > Approximate give you the more meaningful result?
Mentally calculate f(x) for x = 1, then x = 2, then x = 3. Author the line vector(f(x),x,1,5) and simplify the result. What does the vector command do?
Author the line vector([x,f(x)],x,1,5) and simplify the result. What is different between this command and the preceding, and how does the simplfied result differ?
Now author the line vector([x,f(x)],x,1,5,.5) and simplify the result. What is different between this command and the preceding, and how does the simplified result differ? What difference does it make if you choose Simplify > Basic vs. Simplify > Approximate?
Plot the expression that resulted from the preceding question (click on Window > 2-D plot). You can use Set > Plot Range if necessary to change the window of your graph.
Linearizing a Data Set
Author the data set [ [1,1],[2,4],[3,9]] and plot this data set. Note that if you wish to delete previous plots you can use the Edit menu. Is your plot linear?
Author the expression [ [1,1^.5],[2,4^.5],[3,9^.5]] and plot. Is your plot linear? How did this expression differ from the original data set ?
Using the Algebra window fit a straight line to the preceding expression, using the format fit([x, mx+b],#) where # is the line number for the expression [ [1,1^.5],[2,4^.5],[3,9^.5]]. Simplify the result and plot it. Does it fit the points?
Author the expression [[log(1), log(1)], [log(2),log(4)],[log(3), log(9)]]. How does this expression differ from your original data set?
- Simplify and plot this expression. Does the graph form a straight line?
- Fit a straight line to this expression, simplify and plot. Does the plot fit the points you just plotted?
Repeat the preceding for expression [[1, log(1)], [2,log(4)],[3, log(9)]]. How does this expression differ from your original data set and from the preceding expression?
- Simplify and plot this expression. Does the graph form a straight line?
- Fit a straight line to this expression, simplify and plot. Does the plot fit the points you just plotted?
Linearizing another data set:
Repeat all the steps in the exercises under Linearizing a Data Set, but base your work on the data set [[1, 2], [2, 4], [3, 8]].