Science:Math Exam Resources/Courses/MATH110/December 2012/Question 01 (a)/Solution 2

If you've forgotten the rules used in the first solution (or never learned them), you can also use test points. From this picture:

you have the following points, placed in a table of values:

x-value	y-value
0	1
$\pi /2$	0
$\pi$	-1
$3\pi /2$	0

Plugging these same x-values into $f(x)=2\cos(x-\pi )$ gives:

x-value	calculations	y-value
0	$2\cos(0-\pi )=2\cos(-\pi )=2(-1)$	-2
$\pi /2$	$2\cos(\pi /2-\pi )=2\cos(-\pi /2)=2(0)$	0
$\pi$	$2\cos(\pi -\pi )=2\cos(0)=2(1)$	2
$3\pi /2$	$2\cos(3\pi /2-\pi )=2\cos(\pi /2)=2(0)$	0

Drawing a picture based on these points, it should be clear that the graph has been shifted right by $\pi$ and expanded vertically by 2.