Understanding Horizontal Trig Graph Translations

[tg22542]

Quick question guys..
I understand how trig graphs work (cos, sin, tan etc.). What I don't understand is when there is a horizontal translation of say, pi/4, I notice that the graph moves, but I don't really understand how to know exactly how far to move. For example if your HT was pi/4 and your graph was extended on the x-axis -2pi -> 2pi, and the original graph crossed once at -2pi, then where would the new point hit when you apply the translation?

Sorry if that was confusing, any help is appreciated!

 

[CAF123]

Quick question guys..
I understand how trig graphs work (cos, sin, tan etc.). What I don't understand is when there is a horizontal translation of say, pi/4, I notice that the graph moves, but I don't really understand how to know exactly how far to move. For example if your HT was pi/4 and your graph was extended on the x-axis -2pi -> 2pi, and the original graph crossed once at -2pi, then where would the new point hit when you apply the translation?

Sorry if that was confusing, any help is appreciated!

Unless I have misunderstood your question if the original graph intersected x-axis at $-2\pi$ and the translation was $\pi/4$ to the right, then the graph would then intersect at simply $-2\pi + \pi/4$. If it was translated to the left, then it would be $-2\pi - \pi/4$, but this would be outwith your restricted domain $[-2\pi, 2\pi]$

 

[verty]

I'll help with an example.

$f(x) = x^2$
$g(x) = (x - 1)^2 + 3$

$g(x)$ is a translated copy of $f(x)$. How far has it been translated and in which direction? Draw the graphs of $f$ and $g$ if you are not sure.

Then try with $f(x) = 1/x$ and $g(x) = 1/(x - 2) + 3$. Draw these graphs. Do they have the same shape?