10.1.
1) y = 5sin(x – 7) + ( x – 7)^{2}
;
2) y = 5sin x + x^{2}  4.
3) y = –5sin x + x^{2} (change x
to –x).
4) y = 5sin x – x^{2} (change x
to –x and y to –y).
10.2.
1) f(–x) = f(x). Example: y = cos x (in
general, any even function).
2) f(–x) = – f(x). Example: y = sin
x (in general, any odd function).
10.3.
1) Stretch twice over the yaxis;
2) Shrink twice over the xaxis;
3) Shift two units to the left;
4) Reflect over the xaxis.
10.4.
c).
10.5.
The graph consists of three line segments that
connect the following points:
(–4, 2), (–3, 4), (–1, 4) and
(0, 6).
10.6.
It is true because cos satisfies the identity:
cos(–x) = cosx (see EvenOdd Properties
from Lesson 5).
10.7.
10.8.
Draw graphs of sine and cosine:
It is seen that cos
> sin
in the intervals (0, /4)
and (5/4,
2).
10.9.
Draw graph of tan x, then shift it on
/2
to the left and reflect over the yaxis.
10.10.
1) Shift the graph of cosine by 5 units to the
right.
2) Reflect the graph of tangent over the xaxis.
3) Using the main identity (7.6), y = 1. This
is a horizontal line.
4) Using the formula (7.26), y = ½ sin
2x. Shrink the graph of the sine twice along axes
x and y.
10.11.
