G10 Jeopardy

Vocab

100

In the equation Asin(Bx - C) + D, |A| refers to what part?

In the equation Asin(Bx - C) + D, |A| refers to what part?

Amplitude

200

In the equation Asin(Bx - C) + D, D refers to what part?

In the equation Asin(Bx - C) + D, D refers to what part?

Vertical Shift / Midline

300

In the equation Asin(Bx - C) + D, -C/B refers to what part?

In the equation Asin(Bx - C) + D, -C/B refers to what part?

Horizontal Shift / Phase Shift

400

In the equation Asin(Bx - C) + D, 2Pi \ |B| refers to what part?

In the equation Asin(Bx - C) + D, 2Pi \ |B| refers to what part?

Period

500

Explain what a reference number and terminal point are, and give an example of each.

Explain what a reference number and terminal point are, and give an example of each.

Reference number: Angular measure between the point and the closest distance to the x-axis.

Terminal Point: (x, y) coordinates of a point of given radian/degree measure

Logarithms

100

log₃(81) =

log3(81) = 4

200

log₅(0.04) =

log₅(0.04) = -2

300

log(x) = log(225)/log(15)

x = 

log(x) = log(225)/log(15)

log(x) = 2log(15) / log(15)

log(x) = 2

x = 100

400

log₄(x) + log₄(x - 12) = 3

x = 

log₄(x) + log₄(x - 12) = 3

log₄(x(x - 12)) = 3

x(x - 12) = 4³

x² - 12x - 64 = 0 --> (x + 4)(x - 16) ---> x = -4, 16

x = 16 (-4 would be an invalid input)

500

log₄(2x + 1) = log₄(x  + 2) - log₄(3)

x = 

log₄(2x + 1) = log₄(x  + 2) - log₄(3)

log₄(2x + 1) = log₄((x + 2) / 3)

2x + 1 = (x + 2) / 3 ---> 6x + 3 = x + 2

x = -1/5 --> No Solution

Mix

100

What is the reference number of 355 degrees?

What is the reference number of 355 degrees?

5 degrees

200

What is the reference number and terminal point for 2Pi/3 radians?

What is the reference number and terminal point for 2Pi/3 radians?

Ref #: Pi/3

Terminal Point: (-1/2, sqrt(3)/2)

300

For 11Pi/6 radians, give the reference number, terminal point, and quadrant.

For 11Pi/6 radians, give the reference number, terminal point, and quadrant.

Ref #: Pi/6. Terminal Point: (sqrt(3)/2, -1/2). Quadrant: IV.

400

Give the period, amplitude, midline, and phase shift for the function:

y = 3cos(0.5x - 1) - 2

Give the period, amplitude, midline, and phase shift for the function:

y = 3cos(0.5x - 1) - 2

Period = 2Pi / |B| = 4Pi

Amplitude = |A| = 3

Midline = D = -2

Phase Shift = -C/B = 1/0.5 = 2

500

Give the period, amplitude, vertical shift, and horizontal shift and range for the function:

y = -6sin(0.25x + 3) + 7

Give the period, amplitude, vertical shift, and horizontal shift and range for the function:

y = -6sin(0.25x + 3) + 7

Period = 8pi

Amplitude: 6

Vertical shift: 7

Horizontal shift: -12

Range: [1, 13]

Limit Review

100

lim_x->infinity[(2x² - 3x + 6) / (x² + x + 17)] =

lim_x->infinity[(2x² - 3x + 6) / (x² + x + 17)] = 2

200

lim_x->infinity(3x / 2x²)

lim_x->infinity(3x / 2x²) = 0

300

lim_x->-infinity[(x³ - 2x + 1) / (x²  + 5x + 6)] =

lim_x->-infinity[(x³ - 2x + 1) / (x²  + 5x + 6)] = -infinity

400

lim_{x-> 2}[(x² + x - 6) / (x² - 10x + 16)]

lim_{x-> 2}[(x² + x - 6) / (x² - 10x + 16)] = -5/6

500

lim_x->-infinity[sqrt(2x² + 3)] / (2x + 3) =

limx->_-infinity[sqrt(2x² + 3)] / (2x + 3) = -1/sqrt(2)