1. after you factor it should be
2cos 3(x-30) + 4
so the amp is 2, horizontal shift is 30 units right, vertical shift is 4 units up
sorry for the lack of help lol
Please I need help with these questions!
1. tell the amplitude, horizontal shift and vertical shift of
y = 2*cos(3x - pi/2) + 4
2. Find the exact value of the vertical asymptotes for 0<x<pi for the function
y = cot(3x)
3. List the exact amplitude, period and horizontal shift for
y = 2*tan(pi*x + 3)
4. Identif all vertical asymptotes for 0<x<2pi
y = tan(2x - pi/4)
Thank you so much!
we have a vertical asymptote when we attain x-values for which the function is undefined. since x cannot be such values, the graph will approach the line but never touch it. so all we have to do for questions 2 and 4 is find values of x where the function is undefined in the specified limits. i shall demonstrate with 2, try 4 on your own.
2. cot(3x) = cos(3x)/sin(3x)
this function is undefined where sin(3x) = 0
for vertical asymptotes:
sin(3x) = 0
=> 3x = arcsin(0)
=> 3x = 0 + kpi for k an integer
=> x = 0 + k*pi/3 for k an integer
=> x = pi/3 and 2pi/3 for 0 < x < pi ........these lines form vertical asymptotes
the following posts may also help: