Sem 2 Final Review

Asymptotes

100

HA of: (3x)/(2x+5)

y = 3/2

200

HA of: (3x²)/(5x³+x²-6)

y = 0

300

VA of: (x²-3x-4)/(x²+2x-8)

x = -4, x=2

400

VA of: (x+2)/(x²+5x+6)

x = -3

500

VA of: (x²-7)/(x+3)

y = x-3

Logs

100

rewrite in exponential form: log₅x = y

5^y=x

200

Combine into one log: log₃x + log₃15 - log₃4

log₃(15x/4)

300

Combine into one log: 3log₂x - 4log₂y - 2log₂z

log₂(x²/y⁴z²)

400

What asymptote does this log graph have: y = 3log₂(x-1) + 5

VA at x = 1

500

Expand as much as possible: log₄(4x²/(y+16))

1+2log₄x + log₄(y+16)

Domain and Range

100

Domain of: y = 2^x

(-inf, inf)

200

Range of: y = log(x) + 5

(5, inf)

300

Domain of: y = 3/(x²-5x-6)

(-inf, -1) U (-1, 6) U (6, inf)

400

Range of: (x^2 + 8x + 12)/(x+6)

(-inf, -4) U (-4, inf)

500

Range of: (x+3)/(x² + 8x + 15)

(-inf, 0) U (0, 1/2) U (1/2, inf)

Sequences

100

Infinite sum of the sequence: 1/2, 1/6, 1/18,...

S = 3/4

200

Find the common ratio given: a₂ = -6 and a₇ = -192

r=2

300

Write the explicit equation of the sequence: 3, 6, 12, ...

a_n = 3(2)^n-1

400

For an arithmetic sequence, find a₅₀ given a₃ = 26 and a₉ = 14.

a₅₀ = -68

500

Find the 10th term of this sequence: 1/2, -3/8, 9/32,...

a₁₀ = -19683/524288