Department of Math Education
J. Wilson, EMAT 6680

Lesson #1 - by Jan White

For two linear funtions, f(x) and g(x), I will explore h(x) when:

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

h(x)=f(x)*g(x)

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

h(x)=f(g(x))

The sum of two linear functions: f(x) =2x+1 and g(x)=5x+3

h(x)=f(x)+g(x)=7x+4

In general, the sum of two linear functions f(x) +g(x)=h(x) will always be another linear function.

Let f(x) = ax+b
Let g(x) = cx+d
f(x)+g(x) = (ax+b)+(cx+d)
=(a+b)x+(b+d)

The product of two linear functions:  f(x) = 4x +1 and g(x) = 2x + 2

In general, the product of two linear functions, f(x)*g(x) = h(x), will always be a quadratic function.

Let f(x) = ax + b
Let g(x) = cx + d
f(x) * g(x) = (ac)x^2 + (ad +cb)x +bd

The composite of two linear functions: f(x) = 3x + 4 and g(x) = 2x + 1

h(x) = f(g(x)) = 6x +7

In general, the composite of two linear functions will always be a linear function.

Let f(x) = ax + b
Let g(x) = cx + d
h(x) = f(g(x) = a(cx +d) + b

The quotient of two linear equations: f(x) = 3x +1 and g(x) = 4x + 2

h(x) = (3x + 1)/(4x + 2)

Let f(x)= ax +b

Let g(x)=cx+d

h(x)= (ax+b)/(cx+d)

Vertical asymptote is where cx +d=0, x=-d/c

Horizontal asymptote at y=a/c

In general the quotient of two linear functions will always be a rational function with vertical asymptote at -d/c and horizontal asymptote at a/c (c not equal to 0).