James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

chapter 1 Review 69
8. Draw, by hand, a rough sketch of the graph of each function.
(a) y − sin x (b) y − tan x (c) y − e x
(d) y − ln x (e) y − 1yx (f) y − | x |
(g) y − sx (h) y − tan 21 x
9. Suppose that f has domain A and t has domain B.
(a) What is the domain of f 1 t?
(b) What is the domain of f t?
(c) What is the domain of fyt?
10. How is the composite function f 8 t defined? What is its
domain?
11. Suppose the graph of f is given. Write an equation for each of
the graphs that are obtained from the graph of f as follows.
(a) Shift 2 units upward. (b) Shift 2 units downward.
(c) Shift 2 units to the right. (d) Shift 2 units to the left.
(e) Reflect about the x-axis.
(f) Reflect about the y-axis.
(g) Stretch vertically by a factor of 2.
(h) Shrink vertically by a factor of 2.
(i) Stretch horizontally by a factor of 2.
(j) Shrink horizontally by a factor of 2.
12. (a) What is a one-to-one function? How can you tell if a
function is one-to-one by looking at its graph?
(b) If f is a one-to-one function, how is its inverse function
f 21 defined? How do you obtain the graph of f 21 from
the graph of f ?
13. (a) How is the inverse sine function f sxd − sin 21 x defined?
What are its domain and range?
(b) How is the inverse cosine function f sxd − cos 21 x
defined? What are its domain and range?
(c) How is the inverse tangent function f sxd − tan 21 x
defined? What are its domain and range?
true-false quiz
Determine whether the statement is true or false. If it is true,
explain why. If it is false, explain why or give an example that
disproves the statement.
1. If f is a function, then f ss 1 td − f ssd 1 f std.
2. If f ssd − f std, then s − t.
3. If f is a function, then f s3xd − 3f sxd.
4. If x 1 , x 2 and f is a decreasing function, then f sx 1d . f sx 2d
5. A vertical line intersects the graph of a function at most once.
6. If f and t are functions, then f 8 t − t 8 f.
7. If f is one-to-one, then f 21 sxd − 1
f sxd .
8. You can always divide by e x .
9. If 0 , a , b, then ln a , ln b.
10. If x . 0, then sln xd 6 − 6 ln x.
11. If x . 0 and a . 1, then ln x
ln a − ln x a .
12. tan 21 s21d − 3y4
13. tan 21 x − sin21 x
cos 21 x
14. If x is any real number, then sx 2 − x.
EXERCISES
1. Let f be the function whose graph is given.
y
f
1
1
x
(f) Is f one-to-one? Explain.
(g) Is f even, odd, or neither even nor odd? Explain.
2. The graph of t is given.
y
1
g
0 1
x
(a) Estimate the value of f s2d.
(b) Estimate the values of x such that f sxd − 3.
(c) State the domain of f.
(d) State the range of f.
(e) On what interval is f increasing?
(a) State the value of ts2d.
(b) Why is t one-to-one?
(c) Estimate the value of t 21 s2d.
(d) Estimate the domain of t 21 .
(e) Sketch the graph of t 21 .
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