College Algebra 9th txtbk

SECTION 3–3 Transformations of Functions 189
m(x)
5
n(x)
5
p(x)
5
5
5
x
5
x
5
5
x
5
5
5
(d) Cube function
m(x) x 3
Domain: R
Range: R
(e) Square root function
n(x) 1x
Domain: [0, )
Range: [0, )
(f) Cube root function
3
p(x) 1x
Domain: R
Range: R
Z Figure 1 Some basic functions and their graphs.
[Note: Letters used to designate these functions may vary from context to context; R represents the
set of all real numbers.]
Z Shifting Graphs Vertically and Horizontally
If a new function is formed by performing an operation on a given function, then the graph
of the new function is called a transformation of the graph of the original function. For
example, if we add a constant k to f (x), then the graph of y f (x) is transformed into the
graph of y f (x) k.
ZZZ EXPLORE-DISCUSS 1
The following activities refer to the graph of f shown in Figure 2 and the corresponding
points on the graph shown in Table 1.
(A) Use the points in Table 1 to construct a similar table and then sketch a graph
for each of the following functions: y f(x) 2, y f(x) 3. Describe the relationship
between the graph of y f(x) and the graph of y f(x) k for k any
real number.
(B) Use the points in Table 1 to construct a similar table and then sketch a graph
for each of the following functions: y f(x 2), y f(x 3). [Hint: Choose values
of x so that x 2 or x 3 is in Table 1.] Describe the relationship between
the graph of y f(x) and the graph of y f(x h) for h any real number.
B
5
y
Table 1
x
f(x)
5
A
C
D
E x
5
y f(x)
A 4 0
B 2 3
C 0 0
5
D 2
3
Z Figure 2
E 4 0