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 mf + mg and y intercept bf+bg.

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 mf*mg and y intercept mf * bg + bf.

• 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 mf and y intercept at bf +g.

f(x) . g(x) graphs a line with a slope g(mf) and y intercept g(bf).

f(x)/g(x) graphs a line with slope mf/g and y intercept bf/g.

f o g(x) graphs a  horizontal line at mf(g) + b.