Question

Hi could someone please help me with the following question. and please show me how you find each of the properties from the equation. thank you.

State domain, range, period, vertical asymptotes, zeros, symmetry and y-intercept of:
y = -2tan(3x + 180°) + 3.

Answer 1

1) Domain
You want to find any position where you might divide by 0 or take the square root of a negative number.

2) Range
You can take the inverse and try to find the domain of that.
If the inverse is difficult to find out, then try to find the minimum and maximum value of the function, and check if places where the domain isn't defined lead to values that don't occur.

3) Period
You need to find \(p\) such that \(f(x) = f(x + p) = f(x + 2p) = ...\). For \(\sin(x)\) and \(\cos(x)\) the period is \(2\pi\). You can use that fact to try to find periods of more complex functions.

4) Vertical asymptotes
You're gonna find these usually in places when you divide by 0. If your \(y\) coordinate seems to approach positive or negative infinity as as your x coordinate approaches the value that leads to division by 0, then you have a an asymptote.

5) Zeros
Set \(y = 0\) and solve for \(x\). It helps to know the quadratic formula. It also helps to know when certain trig functions equal 0. For \(\cos(x)\) it's \(0, \pi, 2\pi, ...\) for sine it's \(\pi/2, 3\pi/2, 5\pi/2, ...\).

6) Symmetry
I'm not completely sure on this one, because I don't know what is being asked.

6) Y-intercept
Set \(x=0\) and solve for \(y\). This is much easier than zeros because it's just a matter of evaluating the function.

Answer 2

hi for each of the properties, is there anyway you could actually do it for me and show me how to do it? this is a lesson practice question and i dont understand the concept even though i have already read in words how to do it, could you please for each show me how to do it?