Assignment 1: Use a graphing program, such as Graphing Calculator 2.0 or Algebra Xpresser to explore, understand, and extend. Prepare a file of discussion, summary, or graphs to illustrate what you have found.
The problem I chose is as follows.
Make up linear functions f(x) and g(x). Explore, with different pairs of f(x) and g(x) the graphs for
h(x)=f(x)+g(x)
h(x)=f(x)*g(x)
h(x)=f(x)/g(x)
h(x)=f(g(x))
Discussion/Summary/Graphs
The first set of equations are f(x)=x+2 and g(x)=11-2x.
Now, I want to look at the h(x) for the different requirements above.
The second pair of equations are f(x)=x+1 and g(x)=x-1.
Make up linear functions f(x) and g(x). Explore, with different pairs of f(x) and g(x) the graphs for
h(x)=f(x)+g(x)
h(x)=f(x)*g(x)
h(x)=f(x)/g(x)
h(x)=f(g(x))
Case 1: h(x)=f(x)+g(x)
Notice that when we add two linear equations, the results will be a linear equation.
Case 2: h(x)=f(x)*g(x)
In this case a parabola is formed from multiplying two linear equations. Notice that in this case the parabola crosses the x-axis at the points (1,0) and (-1,0).
Case 3: h(x)=f(x)/g(x)
By looking at the equations, it is clear that h(x) will be undefined when x=1. Notice, a hyperbola is formed.
Case 4: h(x)=f(g(x))
In this case, h(x) = x. Notice that the three lines are parallel.