College Algebra 9th txtbk

SECTION 3–3 Transformations of Functions 191
and downward k units if k is negative. We can graph y f(x h) by horizontally shifting
the graph of y f(x) left h units if h is positive and right h units if h is negative.
EXAMPLE 2 Vertical and Horizontal Shifts
The graphs in Figure 5 are either horizontal or vertical shifts of the graph of
Write appropriate equations for functions H, G, M, and N in terms of f.
f(x) |x|.
5
y
G
f
H
5
y
M
f
5
5
x
5
5
N
x
5
Z Figure 5 Vertical and horizontal shifts.
SOLUTION
The graphs of functions H and G are 3 units lower and 1 unit higher, respectively, than the
graph of f, so H and G are vertical shifts given by
H(x) x 3
G(x) x 1
The graphs of functions M and N are 2 units to the left and 3 units to the right, respectively,
of the graph of f, so M and N are horizontal shifts given by
M(x) x 2
N(x) x 3
MATCHED PROBLEM 2
The graphs in Figure 6 are either horizontal or vertical shifts of the graph of
Write appropriate equations for functions H, G, M, and N in terms of f.
f(x) x 3 .
G
y
f H
y
M f N
5
5
5
5
x
5
5
x
Z Figure 6 Vertical and horizontal shifts.
Z Reflecting Graphs
In Section 2-1, we discussed reflections of graphs and developed symmetry properties that
we used as an aid in graphing equations. Now we will consider reflection as an operation
that transforms the graph of a function.