Divide 6x^3 - 18x + 19 by (x - 4) using synthetic division
6x^2 + 24x + 78 + 331/(x - 4)
100
Find the inverse of h(x)
y = (x + 1)^2 - 6
200
Find the domain of f(x)
[-4,-3)U(-3,3)U(3,+infinity)
200
Condense the logarithmic expression
Will be written on board
200
Solve for x
X = -7
X = 2
200
Divide 5x^3 + 6x^2 - x - 2 by (x + 2) using long division
5x^2 - 4x + 7 - 16/(x + 2)
200
Verify whether f(x) and g(x) are inverses of each other
Yes
300
Find the vertical and horizontal asymptotes of f(x)
VA: x = +2 and -2
HA: y = 1/2
300
Solve logarithmic expression for x
X = 3
300
Solve for x, round to nearest tenth (calculator permitted)
X = 5.66
300
Find one positive and one negative coterminal angle for each of the following
A) 315°
B) -420°
C) 7pi/4
A) +675° and -45°
B) +300° and -60°
C) +15pi/4 and -pi/4
300
Solve the given absolute value equation: |x^2 + 6x| = 3x + 18
X = -6, +3, -3
400
Identify the amplitude, period, and horizontal/vertical shifts of f(x)
Amplitude: 8
Period: pi/3
VS: down 1
HS: right pi/3
400
Solve for x
X = ln5
X = ln4
400
Find all the zeros of the given polynomial function f(x)
Zeros are x = 1, 6, -6, 5
400
Knowing that secx = -7/2 and pi/2 < x < pi, find the values of all other 5 trigonometric ratios
cosx = -2/7
sinx = square root of 45 divided by 7
tanx = square root of 45 divided by 2
cscx = 7 times radical 45 divided by 45
cotx = 2 times radical 45 divided by 45
400
Calculate the area of the sector and the length of an arc of a circle, with radius 6cm, intercepted by angle 150°
Area of sector = 5pi
Length of Arc = 15pi
500
Find the domain, vertical/horizontal asymptotes, range, and x/y intercepts of f(x)
Domain: (-infinity,-1)U(-1,2)U(2,+infinity)
Range: (-infinity,2)U(2,+infinity)
VA: x = 2 and -1
HA: y = 2
X intercept: (4,0) (-4,0)
Y intercept: (0,16)
500
Determine whether f(x) is continuous at x = 5 and x = -4. If discontinuous, state the type of discontinuity.
Infinite discontinuity at x = 5
Removable discontinuity at x = -4
500
Find all real and imaginary zeros of f(x)
X = 4, -3, +2i, -2i
500
Evaluate without using a calculator
A) sin300°
B) cot(7pi/6)
C) tan210°
D) cot(5pi/3)
E) csc150°
F) cot(7pi/4)
A) - radical 3 divided by 2
B) radical 3
C) radical 3 divided by 3
D) - radical 3 divided by 3
E) 2
F) -1
500
Solve the given inequality and draw a number line
Zeros: x = 5 and -1
Undefined: x = 2
(-infinity,-1]U(2,5]