# Graphing cos and transformations

I need to graph $y=-2\cos3x$

I just went the standard route and reflected across the x axis, multiplied the y axis by 2 and multiplied the x axis by three. Is this incorrect? I got the wrong answer but I am not sure why.

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What do you mean by "multiplied the $x$-axis by three". Does that mean the waves became steeper or flatter (they should become steeper)? The first two steps sound good, though. – t.b. Jun 13 '11 at 19:42
I mean that if it would normally cross the x axis at pi/2 it would then cross at 3pi/2 I think I just realized this is wrong and it should cross at pi/6 is that correct? – Adam Jun 13 '11 at 19:44
But then you shoud divide the $x$-axis by three. The point is that for $x = \pi/6$ you already have that $3x = 3\pi/6 = \pi/2$. "You run through the $x$ axis three times as fast as usual" due to the factor three: $1/3$ becomes $1$, $1$ becomes $3$, etc, when plugging into $3x$. – t.b. Jun 13 '11 at 19:46
Yes! That's perfectly correct! – t.b. Jun 13 '11 at 19:47
Yes, $-2\cos(3x)$ will cross the $x$-axis at $\pi/6$. – Zev Chonoles Jun 13 '11 at 19:47

What you said sounds correct, though Theo makes a good point that "multiplying the $x$-axis by 3" might be where your problem is. This is what you should be seeing at each step:
Consider what happens when you solve the equation for $x$. You get $x=\frac{1}{3}\ldots$, not $x=3\ldots$. Thus, whatever you mean by "multiplying an axis by a factor", your two multiplications can't both be right, since what corresponds to the factor $2$ for $y$ is a factor of $\frac{1}{3}$ for $x$, not $3$. (Alternatively, you can divide by $2$ to see that what corresponds to the factor of $3$ for $x$ is a factor of $\frac{1}{2}$ for $y$, not $2$.)