Review Jeopardy

Functions and their inverses

100

Is this a function:

(x-5)² + (y+3)² = 9

No.

200

g(x) = 4x^-3/2 - 18x⁵

g^-1(g(x)) = ???

x

300

What are the transformations on:

y(x) = (5/2)(x - 3)² + 48

Vertical stretch: 5/2

Horizontal translation: 3 units right

Vertical translation: 48 units up

400

Domain of:

(x² - 2x + 6)³

----------------

(x-6)(x²+9)

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

500

f(x) = 2x² + 7x^2/3

g(x) = 3x³ + 7

f(g(x)) = ???

2(3x³+7)² + 7(3x³+7)^2/3

Rational Functions and Polynominal Functions

100

Are these lines perpendicular, parallel, or neither:

y₁ = (2/5)x - 1

y₂ = 5x + 2y = 27

Perpendicular

200

Find the vertical / horizontal asymptotes and removable discontinuities:

(x³ + x² - 12x)/(x³ - 9x)

Discontinuities: at x = 0, x = 3

Vertical Asymptote: x = -3

Horizontal Asymptote: y = 1

300

What is the end behavior and leading term of:

f(x) = (1 - 2x⁵)³

End Behavior: x -> inf, y -> -inf

                     x -> -inf, y -> inf

Leading Term: -8x¹⁵

400

How does the multiplicity of the zeros affect the graph of y(x)?

y(x) = (x - 6)²(x + 5)

Bounces at (6, 0).  Goes through (-5, 0).

500

2x² - 9x + 7 = 0

Find x.

x = (9/4) +- (5/4)

Log/Exponential Functions

100

What is the initial value of:

20e^0.3t

20

200

log₂ (x) - log₂ (3) + log₂ (y)

Condense it.

log₂((xy)/3)

300

What is the next step to the problem:

log3(3x + 6) = 81

Apply 3^x to both sides to get:

3x + 6 = log3(81)

400

Find the x-int, y-int:

f(x) = 3(4^x) - 19

x-int: (log₄(19/3), 0)

y-int: (0, -16)

500

log₇ (49^x) = log₃ (1/243)

x = -5/2

Trig: Angles

100

180^o = __ radians

pi

200

Coterminal angle of -362^o

358^o

300

If my given solutions are pi/6 and 2pi/6 in 0 < x < 2pi, what do I add to my solutions to find solutions in a new domain, such as 4pi < x < 6pi

You would add 2pi(k) to both solutions where k is any integer (0, 1, 2, 3)

400

Radians of first quadrant [0^o,90^o]

0, pi/6, pi/4, pi/3, pi/2

500

Solve: cot (sin (pi(cos²(pi/2) + sin²(pi/2))))

undefined

Trig Functions

100

Domain / Range of:

f(x) = cos(x)

Domain: (-inf, inf)

Range: [1, 1]

200

sin (3pi/4)

sqrt(2)/2

300

Solve:

cot^-1(cot(sin(-11pi/6)))

 = sin(-11pi/6)

2pi - 11pi/6 = pi/6 

sin(pi/6) = 1/2

400

Find

cos^-1(-sqrt(2)/2)

rewrite as cos(x) = -sqrt(2)/2

x = 3pi/4 and 5pi/4

500

cot(x) / csc(x)

cos(x)