Transformation of trigonometry functions

[chwala]

Homework Statement

let $f(x)= (\sin 2x + \cos 2x)^2$ and $g(x)= cos 2x-1$ The graph of $y=g(x)$ can be obtained from the graph of $y=f(x)$ under a horizontal stretch of scale factor $k$ followed by a translation of vector $(p,q)$, find the exact values of $k, p, q$

Relevant Equations

horizontal and vertical stretch....

kindly note that this solution is NOT my original working. The problem was solved by my colleague. I have doubts with the $k$ value found. Is it not supposed to be $k=0.5?$ as opposed to $k=2?$. From my reading on scaling, the graph shrinks when $k$ is greater than $1$ and conversely.

 

[BvU]

Homework Statement:: let $f(x)= (sin 2x + cos 2x)^2$ and $g(x)= cos 2x-1$ The graph of $y=g(x)$ can be obtained from the graph of $y=f(x)$ under a horizontal stretch of scale factor $k$ find the exact values of $k, p, q$

You also want to tell us what $p$ and $q$ are !

$\LaTeX$ tip: use \sin and \cos

 

[chwala]

You also want to tell us what $p$ and $q$ are !

$\LaTeX$ tip: use \sin and \cos

sorry, i just amended the question...

 

[Doc Al]

From my reading on scaling, the graph shrinks when $k$ is greater than $1$ and conversely.

That's certainly true, but check it for yourself: Plot $sin (x)$ vs $sin (2x)$.

 

[Mark44]

the graph shrinks when k is greater than 1 and conversely.

A better way to say this, regarding f(kx) vs. f(x) is this:
Horizontal compressions/expansions
If k > 1, the graph of y = f(kx) is the compression of the graph of y = f(x) toward the vertical axis.
If 0 < k < 1, the graph of y = f(kx) is the expansion of the graph of y = f(x) away the vertical axis.

Vertical compressions/expansions
If k > 1, the graph of y = k* f(x) is the expansion of the graph of y = f(x) away from the horizontal axis.
If 0 < k < 1, the graph of y = k* f(x) is the compression of the graph of y = f(x) toward the horizontal axis.

For negative values of k, there are reflections happening, which is a different matter.