ASSIGNMENT
1

**Heather J. Robinson**

**EMAT 6680, Fall 2003**

Linear functions can occur in one of two forms:

- Form
#1: f(x) = k where k is a
real number, or
- Form
#2: f(x) = mx+b where m is
not equal to 0.

In
exploring operations of addition , multiplication , division , and composition with pairs of linear
functions , f(x)
and g(x), three cases can evolve from these two forms of linear functions.

*Case
1: f(x) = mx+b and g(x) =
mx+b*

# Let f(x) = 3x + 2 and g(x) = x - 1

f(x) + g(x) graphs a line with
slope m_{f} + m_{g} and y intercept b_{f}+b_{g}.

f(x) ^{.} g(x) graphs a parabola.

f(x)/g(x) graphs a function with
horizontal asymptote at 3/1 and vertical asymptote at x = 1.

f ^{o }g(x) graphs a line
with a slope m_{f}*m_{g} and y intercept m_{f} * b_{g}
+ b_{f}.

*Case
2: f(x) = k and g(x) = z*

# Let f(x) = -2 and g(x) = 4

f(x) + g(x) graphs a horizontal
line at k + z.

f(x) ^{.} g(x) graphs a horizontal line at k ^{.} z.

f(x)/g(x) graphs a horizontal line
at k/z.

f ^{o }g(x) graphs a
horizontal line at k.

* *

* *

*Case
3: f(x) = mx+b and g(x) = k*

## Let f(x) = 3x - 2 and g(x) = 4

f(x) + g(x) graphs a line with a
slope m_{f} and y intercept at b_{f} +g.

f(x) ^{.} g(x) graphs a line with a slope g(m_{f})
and y intercept g(b_{f}).

f(x)/g(x) graphs a line with slope
m_{f}/g and y intercept b_{f}/g.

f ^{o }g(x) graphs a horizontal line at m_{f}(g) +
b.

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