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Answers To The Exercises: 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14
Lesson 10
 


10.1.
1) y = 5sin(x – 7) + ( x – 7)2 ;
2) y = 5sin x + x2 - 4.
3) y = –5sin x + x2 (change x to –x).
4) y = 5sin x – x2 (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 y-axis;
2) Shrink twice over the x-axis;
3) Shift two units to the left;
4) Reflect over the x-axis.

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 Even-Odd 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 y-axis.

10.10.
1) Shift the graph of cosine by 5 units to the right.
2) Reflect the graph of tangent over the x-axis.
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.

 

 

 

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