Domains and Ranges of Trig and Inverse Trig
Domain of
f(x) = \sin(x) +1
\mathbb{R}
\cos(\frac{4\pi}{3})=
-\frac{1}{2}
The length of the side opposite the 30^{\circ} angle in a 30-60-90 triangle with a hypotenuse of length 6.
3
Determine which of the following are rational functions (can be multiple):
f(x) = \frac{x^2+2}{x}
g(x) = -7
h(x) = -9x^3+x^2-7x+1
All of them
Determine the horizontal asymptote(s) of
f(x) = \frac{-3x^3-2x+1}{x^4+7}
Horizontal asymptote at
y=0
Range of
f(x)=arcsin(x)
[-\frac{\pi}{2},\frac{\pi}{2}]
\cos(\arccos(-\frac{\sqrt{3}}{2}))=
-\frac{\sqrt{3}}{2}
Solve for x:
tan(x)+3=2
x=\frac{3\pi}{4}+\pi k
for k an integer
Determine the y-intercept of
f(x) = \frac{2x^2-8x}{x^4+6}
(0,0)
Determine the horizontal asymptotes of
f(x) = \frac{x^6+1}{x^2-9}
No horizontal asymptotes
Range of
f(x) = \arctan(x)
(-\frac{\pi}{2},\frac{\pi}{2})
\arccos(\tan(\frac{3\pi}{4}))=
\pi
Quadrant in which an angle of 2.5 radians lies.
Quadrant II
Domain of
f(x)=\frac{x^3-2x+7}{x^2+5x-14}
in interval notation
(-\infty,-7)\cup(-7,2)\cup(2,\infty)
Find all holes (removable discontinuities) of
f(x) = \frac{(x+1)(x-1)}{x^2-3x+2}
Hole at
(1,-2)
Domain of
f(x) = -\arccos(x-1)+2
[0,2]
\arcsin(\sin(\frac{16\pi}{3}))=
-\frac{\pi}{3}
Asymptotes of
f(x) = \tan(x+\frac{\pi}{4})+1
Vertical asymptotes at
x=\frac{k\pi}{2}-\frac{\pi}{4}
for all odd integers
k
Determine the x-intercepts of
f(x)=\frac{x^2+2x-3}{x^2+4x+3}
(1,0)
Determine the vertical asymptotes of
f(x) = \frac{(x+1)(x-1)}{x^2-3x+2}
Vertical asymptote at
x=2
Domain of
f(x) = \sin(\arccos(2x)) + \cos(\arcsin(8x+3))
[-\frac{1}{2},-\frac{1}{4}]
\sin(\arctan(-\frac{12}{5}))=
-\frac{12}{13}
Angle in radians rotated once an object has moved
2/9 of the way around the perimeter of the unit circle.
\theta = \frac{4\pi}{9}
\lim_{x\to 1}\frac{(x+2)(x+1)}{(x-1)(x-3)}=
DNE (limit from left is \infty and limit from right is -\infty )
Determine all holes and vertical asymptotes of
f(x) = \frac{(x-7)(x+2)}{3x^2+4x-4}
Vertical asymptote at x=2/3 and hole at (-2,\frac{9}{8})