####

#### Lastly let's investigate h(x) = f(g(x)) when n = 0

#### f(x) = -3

#### g(x) = 5

#### h(x) = n(nx + 5) - 3, therefore h(x) = -3

####

#### Again we start out with straight lines.

####

#### However, what happens when we make n=6

#### f(x) = 6x - 3

#### g(x) = 6x + 5

#### h(x) = 6(6x +5) - 3

####

#### Again we get a straight line.
Let's compare the slopes and y-intercept as we did in the first
investigation

#### f(x) = 6x - 3

#### g(x) = 6x + 5

#### h(x) = 6(6x +5) - 3

#### h(x) = 36x + 30 - 3

#### h(x) = 36x + 27

#### Therefore, the slope is the
product of the slopes of f(x) and g(x) and the y-intercept is
the product of the slope of f(x) and the y-intercept of g(x)
plus the y-intercept of f(x)

####

#### Will this stand true when we
set n = 20

#### f(x) = 20x - 3

#### g(x) = 20x + 5

#### h(x) = 20(20x + 5) - 3

####

#### h(x) = 20(20x+5) - 3

#### h(x) = 400x + 100 - 3

#### h(x) = 400x + 197

#### with the slope equal to 400
and the y-intercept equal to 197

#### Will the composition always
be a linear function? Let's look at the general case

#### f(x) = ax + b

#### g(x) = cx + d

#### h(x) = a(cx + d) + b

#### h(x) = (ac)x + ad + b

#### h(x) = (ac)x + (ad +b)

#### if

#### s = ac

#### t = (ad + b)

#### then we get

#### h(x) = sx + t

#### a linear function

####