Functions Worksheet With Answer Key Page 27
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4695
2.4 PREVIEW OF TRANSFORMATIONS: SHIFTS
Exercises
1. Using Table 2.14, complete the tables for g, h, k, m,
3. y = f (x + 2)
4. y = f (x) + 2
where:
5. y = f (x
1)
5
6. y = f (x + 6)
4
(a) g(x) = f (x
1)
(b) h(x) = f (x + 1)
(c) k(x) = f (x) + 3
(d) m(x) = f (x
1) + 3
Explain how the graph of each function relates to the
graph of f (x).
7. The graph of f (x) contains the point (3, 4). What point
must be on the graph of
Table 2.14
(a) f (x) + 5?
(b) f (x + 5)?
x
2
1
0
1
2
f (x)
3
0
2
1
1
(c) f (x
3)
2?
x
1
0
1
2
3
8. The domain of the function g(x) is
2 < x < 7. What
g(x)
is the domain of g(x
2)?
x
3
2
1
0
1
9. The range of the function R(s) is 100 ≤ R(s) ≤ 200.
h(x)
What is the range of R(s)
150?
x
2
1
0
1
2
10. (a) Using Table 2.15, evaluate
k(x)
(i) f (x) for x = 6
x
1
0
1
2
3
(ii) f (5)
3
m(x)
(iii) f (5
3)
(iv) g(x) + 6 for x = 2
2. Figure 2.27 shows f (x). Graph y = f (x + 3) + 3. Label
all important features.
(v) g(x + 6) for x = 2
y
(vi) 3g(x) for x = 0
4
(vii) f (3x) for x = 2
f
(viii) f (x)
f (2) for x = 8
x
(ix) g(x + 1)
g(x) for x = 1
5
3
(b) Using the values in the table, solve
(i) g(x) = 6
(ii) f (x) = 574
4
(iii) g(x) = 281
Figure 2.27
(c) The values in the table were obtained using the for-
3
2
mulas f (x) = x
+ x
+ x
10 and g(x) =
2
7x
8x
6. Use the table to find two solutions
In Exercises 3–6, use Figure 2.28 to graph the transformation
3
2
2
to the equation x
+ x
+ x
10 = 7x
8x
6.
of f .
y
5
Table 2.15
4
3
f (x)
x
0
1
2
3
4
5
6
7
8
9
2
f (x)
10
7
4
29
74
145
248
389
574
809
1
g(x)
6
7
6
33
74
129
198
281
378
489
x
0
1
2
3
4
5
6
Figure 2.28
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