Eunju Jung, Department of Mathematics

Exploring the linear functions

Problem 2

Make up linear functions f(x) and g(x). Explore, with diffefent pairs of f(x) and g(x) the graphs for

1.) h(x) = f(x) + g(x)

2.) h(x) = f(x).g(x)

3.) h(x) = f(x)/g(x)

4.) h(x) = f(g(x))

Summarize and illustrate.

Let's make up the linear functions such as f(x)=ax+b and g(x)=cx+d.

Algebraically, we can simplify as below:

The addition and composition of the two linear functions are linear equations, and the multipication is

the quadratic equation. In the case of division, we can observe that there is an asymptote at x=-d/c.


Here are some examples.


Let f(x)=2x+b and g(x)=-4x+d where b and d are 1,2,3,4,5.


Case 1) f(x)+g(x)


Case 2) f(x).g(x)



Case 3) f(x)/g(x)



Case 4) f(g(x))