College Algebra 9th txtbk

198 CHAPTER 3 FUNCTIONS
ANSWERS TO MATCHED PROBLEMS
1. (A) The graph of y 1x 3 is the same as the graph of y 1x shifted upward 3 units, and
the graph of y 1x 1 is the same as the graph of y 1x shifted downward 1 unit. The
figure confirms these conclusions.
(B) The graph of y 1x 3 is the same as the graph of y 1x shifted to the left 3 units,
and the graph of y 1x 1 is the same as the graph of y 1x shifted to the right 1
unit. The figure confirms these conclusions.
5
5
y
5
y x 3
y x
y x 1
x
5
5
y
5
y x 3
y x
y x 1
x
5
5
2. G(x) (x 3) 3 , H(x) (x 1) 3 , M(x) x 3 3, N(x) x 3 4
3. (A) The graph of y f(x) is the (B) The graph of y f(x) is the
reflection through the x axis of reflection through the y axis of the
the graph of y f(x).
graph of y f(x).
y
y
5
(2, 4)
5
(2, 4) (2, 4)
y f(x)
5
5
x
y f(x)
5
y f(x)
5
x
y f(x)
(2, 4)
5
5
(C) The graph of y f(x) is the
reflection through the origin of
the graph of y f(x).
5
y
(2, 4)
y f(x)
5
5
x
(2, 4)
5
y f(x)
4. (A) The graph of y 2f(x) is a
vertical stretch of the graph of
y f(x) by a factor of 2. The
graph of y 1 2 f (x) is a vertical
shrink of the graph of y f(x)
by a factor of 1 2.
(B) The graph of y f(2x) is a
horizontal shrink of the graph of
1
y f(x) by a factor of 2.
The graph of y f ( 1 2 x) is a
horizontal stretch of the graph
of y f(x) by a factor of 2.