College Algebra 9th txtbk

SECTION 3–3 Transformations of Functions 201
71.
y
76.
y
5
5
5
5
x
5
5
x
5
5
72.
y
77.
y
5
5
5
5
x
5
5
x
5
5
73.
y
78.
y
5
5
5
5
x
5
5
x
5
5
74.
75.
5
5
5
5
5
5
5
5
y
y
x
x
79. Consider the graphs of f(x) 18x
3 and g(x) 21x
3 .
(A) Describe each as a stretch or shrink of y 1x
3 .
(B) Graph both functions in the same viewing window on a
graphing calculator. What do you notice?
(C) Rewrite the formula for f algebraically to show that f and
g are in fact the same function. (This shows that for some
functions, a horizontal stretch or shrink can also be interpreted
as a vertical stretch or shrink.)
80. Consider the graphs of f(x) (3x) 3 and g(x) 27x 3 .
(A) Describe each as a stretch or shrink of y x 3 .
(B) Graph both functions in the same viewing window on a
graphing calculator. What do you notice?
(C) Rewrite the formula for f algebraically to show that f and
g are in fact the same function. (This shows that for some
functions, a horizontal stretch or shrink can also be interpreted
as a vertical stretch or shrink.)
81. (A) Starting with the graph of y x 2 , apply the following
transformations.
(i) Shift downward 5 units, then reflect in the x axis.
(ii) Reflect in the x axis, then shift downward 5 units.
What do your results indicate about the significance of
order when combining transformations?
(B) Write a formula for the function corresponding to each of
the above transformations. Discuss the results of part A in
terms of order of operations.