Show:
Vectors &
Complex Numbers
Polar & Rectangular
Coordinates
Functions &
Rational Functions
Exponential &
Logarthmic Functions
Miscellaneous
100
What is the formula to find a unit vector, u, in the direction of a vector, v?
The unit vector is given by: u = v / ||v||
100
Convert this point in polar coordinates to rectangular coordinates: (r, theta)= (2, pi)
(x, y) = (-2, 0)
100
Identify the Parent Function and Describe the transformations of: f(x) = sqrt(-x + 3)
reflect across y-axis Horiz shift R by 3 units
100
What is the exponential form of: log base 32 of 4 = 2/5
32^(2/5) = 4
100
Is f(x) even, odd, or neither? f(x) = - (x-8)^2
neither
200
If the dot product of two vectors equals zero, then the two vectors are:
orthogonal (or perpendicular)
200
Convert this point in rectangular coordinates to polar coordinates: (x, y) = (0, -5)
(r, theta) = (5, 3pi/2) OR (r, theta) = (-5, pi/2)
200
What is the Domain of f(x)? f(x) = -4 / (sqrt(2x-7))
x > 7/2
200
What is the logarithmic form of this equation: 9^3/2 = 27
log base 9 of 27 = 3/2
200
What are the Vertical Asymptote(s) of f(x): f(x) = (2x^2 + 7x + 6) / x^2 - 2x - 8
VA at x=4. Hole at x=-2
300
Find a unit vector in the direction of <-2, 5>
< -2/sqrt(29), 5/sqrt(29)>
300
What is the rectangular form of this polar equation? r = 5
x^2 + y^2 = 25
300
If f(x) = x+2 and g(x) = 4-x^2 what is (f of g)(x) ? and evaluate at x=2.
(f of g)(x) = 6-x^2 (f of g)(2) = 2
300
What is x? log base 16 of 8 = x
x = 3/4
300
What is the slope - intercept form of a line passing through: (-5, 7) and (3, 5)
y = -0.25x + 23/4 = -0.25x + 5.75
400
Initial Point P: (-3, 1) Terminal Point Q: (4, 5) Write the vector PQ as a linear combination of standard unit vectors, i and j.
PQ = < 7, 4 > = 7i + 4j
400
What is the rectangular form of this polar equation? r = sec(theta)
x = 1
400
What is the inverse of f(x) = (5-3x) / 2
f^-1(x) = (5-2x) / 3
400
Condense this expression: 2ln(x) + ln(x+1)
ln(x^2(x+1))
400
What is the slope-intercept form of a line perpendicular to y=-4x + 3 that goes through the point (4, 9)?
y = 0.25x + 8
500
Find the angle between u = < 4, 3 > and v = < 3, 5 >
cos(theta) = (u dot v) / ( ||u|| ||v|| ) theta = cos^-1 (27/5sqrt34) = 22.2 degrees
500
What is the Polar form of this equation? x^2 + y^2 - 6x = 0
r = 6 cos(theta)
500
What is the equation of the slant asymptote for: f(x) = (x^2 + 5x + 6) / (x-4)
y = x+9
500
Expand this Expression: log base8((x^4 (x+3)^2)/(x^2 - 7)
4log base8(x) + 2 log base8(x+3) - log base8(x^2 -7)
500
Name 3 things that Mrs. K grows in her garden
Peas, Asparagus, Basil, Tomatoes, Garlic, Beans, Cukes, Squash, Oregano, Rhubarb, Sunchokes, Swiss Chard, Carrots