Need help with pre-calc

[worldly kindle]

Please help me if you can

[analog trellis]

you are posting your whole assignment here😆

[worldly kindle]

just need help with number 1a-1e

[lusty ibex]

A) aren't both possible? Because tan(π/2 -x) =cot(x)
B)at x=-π/3, y=-♾️
And at x=π/3, y=-♾️
So, the function repeats after an interval of 2π/3, so that is the period

C)at some points, the value of y tends to -♾️ and for other values of x, y tends to +♾️

Therefore, the range of y is from -♾️ to +♾️, which is the vertical stretch of the graph

[lusty ibex]

E) we'll consider the graph to be in the form of y=tan(ax+b)+c, where a abd b are finite constants

At x=0, y=tan(b)+c, which is -2, according to the graph

At x=π/3, y=♾️ which is tan 90°
So, tan(a.π/2 +b) +c = not defined, so aπ +b = nπ+π/2, where n is an integer
Similarly, a(5π/3) +b = (n+1)π +π/2, since it is the next time y=♾️

By subtracting the two equations we get 2πa/3=π, which means a=3/2

At x=π/3, y=♾️, right?
So, tan(aπ/3 +b)+c=♾️,
Substitute a=3/2 so we get b= nπ

At x=0, y=-2 so, tan (0+nπ) +c= -2
So, 0 +c=-2, and this c=-2

Tan(3xπ/2+ nπ) = tan(3πx/2)

So, the equation is y =tan(3πx/2) - 2

D) the vertical shift is just c, which is -2

Hope it helped, I explained it in the simplest way i could

[austere rune]

i appreciate your effort, but we're helpers instead of HW-doers
please give hints/guide instead of complete solution