Foundational + Random
The domain of f o g:
f(x) = √(x-5)
g(x) = √(5-x)
[0,5]
If the roots of a polynomial has the degrees...
x = -2, Degree 3
x = 0, Degree 1
x = 1, Degree 2
What is the End behavior to the right if the left of the graph goes towards +infinity
x --> +infinity
f(x) --> +infinity
If a Vertical asympote of a rational function has a degree of 2 what is the behavior?
Opposite directions
The domain of log(3x-4)
3x - 4 > 0
x > 4/3
The reference angle and quadrant of -9π/4
π/4 and Quadrant 4
Describe the transformation in order of
f(x) = (x+1)/(x-4)
Horizontal shift to the right by 4
Vertical compression by 2
Vertical Shift up by 1
The end behaviors of -x5-3x+2
Right -> Negative infinity
What do you need to graph a rational function?
1. X-y intercept
2. VA and HA
3. Behaviors near asymptotes
4. Behaviors near roots
How many times stronger is a magnitude 8 earthquake compared to magnitude 4?
8 = 2/3 log (S1/1016)
- 12 = log (S1/1016)
- 1012 = S1/1016
- S1 = 1028
4 = 2/3 log (S2/1016)
- 6 = log (S2/1016)
- 106 = S2/1016
- S2 = 1022
A fidget spinner with a radius of 2 inch, is rotating at 85RPM, what is its speed?
v = r w
w = 85 rotations/min x 2π radians/1 rotation
w = 533.8
v = 2 x 533.8 = 1067.6
The roots of
f(x) = x2 - 8x - 20
4 ± 2i
If the following function is divided by x + 2, is there a remainder? If there is, what is it?
f(x) = -4x3 + 8x2 + 12x + 16
Remainder theorem f(-2) = 56
Horizontal and Vertical Asymptotes of
(x2-3x-4)/(x2 - 2x - 8)
HA = 1
VA = -2
f(x) = -4(1/8)x -1
Downward towards the x axis
Reflect, so upwards towards the x axis
Vertical stretch by 4
Vertical Shift down by 1
New HA is at -1
If cos(θ) = -5/8 and θ is in II quadrant, what is sin(θ) and tan(θ)
sin(θ) = √39/8
tan(θ) = -√39/5
What is the domain when f(x) > 0
f(x) = |x2 - 4| -1
|x2 - 4| - 1 > 0
|x2 - 4| < 1
x2 - 4 = 1
- x = ±√5
x2 - 4 = -1
= ±√3
Number line will show...
x is [(-infinity, -√5)U(-√3, √3)U(√5, +infinity)
What are the possible roots and the interval of the roots:
f(x) = x3 +3x2 - 14x + 8
Max = 14
Cauchy = -14/1 -1 , 14/1+1 = [-15,15]
Rational Root Theorem:
p = 8 --> ±4, ±2, ±8, ±1
q = 1 --> ±1
{4, -4, 2, -2, 8, -8, 1, -1}
The domain of
√(x-1)(x-2)/(x-3)
[1,2]U(3, infinity)
Solve for x:
3ln(x)2 + 2(lnx2) = 4
ln(x) = u
3u2 + 4lnx - 4 = 0
(3u - 2)(u + 2)
ln(x) = 2/3 --> e2/3
ln(x) = -2 --> e-2
tan2x sin2x= tan2x - sin2x
(sec2x -1)sin2x
sin2x/cos2x - sin2x
tan2x - sin2x