Domain and Range
f(x)=3x^2 -5
D: ARN R: [-5, oo)
Find solutions between
[0, 2pi)
for
4cos^2(x)=1
x=pi/3, (2pi)/3, (4pi)/3, (5pi)/3
Find all intercepts for
f(x)=(x^2-1)/(3x+1)
x=
+-1
y=
-1
A right triangle has a hypotenuse of 4 and one angle measuring 45 degrees. Draw a diagram including all angles and side-lengths.
45 degrees, 2.82, 2.82
f(x)=sqrt(x-4)-2
D: [4, oo) R: [-2, oo)
(x^2-5x)/(3-3x)=1
x=-1, 3
Find all asymptotes for
f(x)=(x-1)/(4+x^2)
y=0
A right triangle has a hypotenuse of 5 and side-length 3. Draw a diagram of the triangle including all angles and side-lengths.
4, 36.87 degrees, 53.13 degrees
f(x)=1/sqrt(x^2-4)
D: (-oo, -2)U(2, oo) R: (0, oo)
2-log(x+5)=1
x=5
Find the vertex of
f(x)=x^2-5x+6
(2.5, -.25)
The angle of elevation to the top of a building from a point 300 feet away is 60 degrees. Find the height of the building.
520 feet
f(x)=2-e^x
D: ARN R: (-oo, 2)
tanxsin^2x=tanx
x=0, pi
How many cycles does the function complete on the interval?
[-2pi, 2pi]
f(x)=2sin(1/2x)
One
A wire stretches from the top of a vertical pole to a point on level ground 16 feet from the base of the pole. If the wire makes an angle of 62 degrees with the ground, find the height of the pole AND the length of the wire.
34 feet, 30 feet
f(x)=3cos(x-pi)+1
D: ARN R: [-4, 2]
cot^2x=3
x=pi/6, (5pi)/6, (7pi)/6, (11pi)/6
How many asymptotes does the function have on the interval?
[-pi, pi]
tan(x/4)
None
A right triangle has one angle of 30 degrees. Draw a diagram of the triangle including all angles and side-lengths.
60 degrees, 1, 2,
sqrt3