Algebra 2 Semester 2 Review

Inverses

100

Find the inverse of the function:

f(x) = 2x³ + 3

cube root ( (x - 3) / 2)

200

Rewrite in logarithmic form:

x^y = 101

log_x101 = y

300

Evaluate the logarithm:

log₆(1/216)

-3

400

Rewrite in exponential form:

log₅50 = k

5^k = 50

500

State if the following functions are inverses:

f(x) = (2/(n+1)) + 1
g(x) = (1/(n+1)) + 2

no

Logarithms

100

Expand the logarithm:

log(ab)²

2 log(a) + 2 log(b)

200

Condense the logarithm:

log₃u - 5 log₃v

log₃(u/v⁵)

300

Condence the logarithm:

20 log₆x + 5 log₆y

log₆(x²⁰y⁵)

400

Expand the logarithm:

log₄(xy/z)

log₄x + log₄y - log₄z

500

Condense the logarithm:

2(log₅a + log₅b) - log₅c

log₅((a²b²)/c)

Trigonometry

100

What is the starting point for the function:

y = 4cosθ

(0,4)

200

What is the midline for the function:

y = 3sinθ-2

y=-2

300

What is the period of the function:

y = tan3θ

π/3

400

Describe the phase shift AND vertical shift of the function:

y = 4 sin (θ - π/4) - 1

Phase shift: right π/4

Vartical shift: down 1

500

What is the starting/center point for the function:

y = 3 cos (θ + π) + 2

(-π, 5)

Polynomials

100

Classify the polynomial by degree and number of terms:

2n² - 2 + 3n

quadratic trinomial

200

Find the zeros of the polynomial:

f(x) = 2x⁴ + 2x³ - 12x²

x = {2, 0 (mult, 2), -3}

300

Divide:

(2x² + 5x - 42) / (x + 6)

2x - 7

400

Divide:

(6a² + 24a - 36) / (a + 5)

6a - 6 - (6/(a+5))

500

Divide:

(k³ - 17k + 8) / (k - 4)

k² + 4k - 1 + (4/(k-4))

Imaginary #s

100

Simplify the expression:

(6 + i) (-8 + 3i)

-51 + 10i

200

Find the aboslute value of the complex number:

|2 - 4i|

2 sqrt(5)

300

Sketch a graph with one real root and two complex roots.

*on graph*

400

Find the equation of the function that has the roots: 

(2 + 5i) and (2 - 5i)

y = x² - 4x + 29

500

Solve using the quadratic formula:

0 = x² - 6x + 12

3 +/- i sqrt(3)