Unit 8
MHF 4U1
Lesson 6– Sums and Differences of Functions
Recall:
 Some polynomials are symmetrical about the y-axis. These are even functions
where f ( x)  f ( x) .
 Some polynomials are have rotational symmetry about the origin. These are odd
functions, where f ( x)   f ( x) .
 Most polynomial functions have no symmetrical properties. These are functions
that are neither even nor odd, with no relationship between f ( x) and f (x ) .
Two functions f(x) and g(x) can be combined through addition or subtraction to create a
new combined function.
SUM
DIFFERENCE
(f + g)(x) = f(x) + g(x)
(f – g)(x) = f(x) – g(x)
 The graph of f + g can be obtained
by adding the y-coordinates of f
and g.
 The domain of f +g is the
intersection of the domains of f
and g. The function is only
defined where the two graphs
overlap.
 The graph of f - g can be obtained
by subtracting the y-coordinates
of f and g.
 The domain of f - g is the
intersection of the domains of f
and g. The function is only
defined where the two graphs
overlap.
Example 1:
Let f  (1,2), (0,3), (1,4), (2,3), (4,1) and
g  (1,3), (0,2), (2,2), (3,4)
Determine f  g and f  g .
Example 2: Given that f ( x) 
1
1
and g ( x) 
.
x3
x3
a) What is f  g and what is it’s domain?
Unit 8
MHF 4U1
b) What is f  g and what is it’s domain?
c) What is ( f  g )(5) ?
Example 3: Given the graphs of f(x) and g(x) as shown, sketch the graphs of (f + g)(x)
and (f – g)(x) where 0  x  3 .
.