Finals Review

Foundational + Random

Power and Polynomial

Rational Functions

Logarithms and Exponentials

Trigonometric Functions

100

The domain of f o g:

f(x) = √(x-5)

g(x) = √(5-x)

[0,5]

100

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

100

If a Vertical asympote of a rational function has a degree of 2 what is the behavior?

Opposite directions

100

The domain of log(3x-4)

3x - 4 > 0

x > 4/3

100

The reference angle and quadrant of -9π/4

π/4 and Quadrant 4

200

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

200

The end behaviors of -x⁵-3x+2

Left -> + Infinity

Right -> Negative infinity

200

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

200

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

<-> 10²⁸/10²² = 10⁶ times stronger

200

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

300

The roots of

f(x) = x²- 8x - 20

4 ± 2i

300

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

300

Horizontal and Vertical Asymptotes of

(x²-3x-4)/(x² - 2x - 8)

HA = 1

VA = -2

300

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

300

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

400

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)

400

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}

400

The domain of

√(x-1)(x-2)/(x-3)

[1,2]U(3, infinity)

400

Solve for x:

3ln(x)² + 2(lnx²) = 4

ln(x) = u

3u²+ 4lnx - 4 = 0

(3u - 2)(u + 2)

ln(x) = 2/3 --> e^2/3

ln(x) = -2 --> e^-2

400

tan²x sin²x= tan²x - sin²x

(sec²x -1)sin²x

sin²x/cos²x - sin²x

tan²x - sin²x