Skylar M. Christensen's 5th Hour - Jeopardy

Function Operations and Composition

100

g(x) =x³ + x

h(x) = x + 5

Find g(x) + h(x)

x³+2x+5

200

f (x) = x + 5

g(x) =x² + x

Find f (x) - g(x)

-x² + 5

300

g(t) = t² + 3t

f (t) = 3t - 4

Find g(t) × f (t)

3t³ + 5t² - 12t

400

g(x) = -4x + 4

h(x) =x³ + 4x²

Find g(x) × h(x)

-4x⁴ - 12x³ + 16x²

500

g(t) = 4t - 3

f (t) = t² - t

Find g(f(t)) 

t² - 4t - 3

Inverse Functions

100

Find the inverse.

(1, -3), (-2, 3), (5, 1), (6, 4)

 (-3, 1), (3, -2), (1, 5), (4, 6)

200

Find the inverse.

(-5, 7), (-6, -8), (1, -2), (10, 3)

 (7, -5), (-8, -6), (-2, 1), (3, 10)

300

Find an equation for the inverse

y = 3x + 2

y= (x-2)/3 

400

Find an equation for the inverse

y=-3/4x+5

y= -4/3x + 20/3

500

Find an equation for the inverse

y= x² - 4

y= + or - √ x+4

Graphing and Solving Polynomials

100

What is the end behavior of this equation.

y = 6x⁵ + 4.3x³ + 2.8x +.03

Since the degree is odd and the coefficient is positive, the end behavior is down to the far left and up to the far right.

200

What is the end behavior of this equation.

y = -2x⁴ + 5x⁴ - 3

Since the degree is even and the coefficient is negative, the end behavior is down to the far left and down to the far right.

300

Graph the Equation. 

What are the zero(s) and what is the minimum and maximum?

x³ + 11x² + 35x + 32

Min = (-2.3 , -2.5 )

Max= (-5 , 7)

Zeros- (-6.2 , 0) (-3.2 , 0) (-1.6, 0)

400

Graph the Equation. 

What are the zero(s) and what is the minimum and maximum?

f(x)= x² + 2x -5

Min = (-1,-6)

Max= infinite 

Zeros- -3.4 , 1.4

500

Graph the Equation. 

What are the zero(s) and what is the minimum and maximum?

x³ + x² - x - 2

Min = (0.3 , -2.2)

Max= (-1 , -1)

Zeros- (1.2 , 0)

Solving Exponential and Logarithmic Equations

100

Solve the Equation

2log₈x = -2

1/8 

200

Solve the Equation 

log₈n = 2

64

300

Solve the Equation

ln(2k + 7) = ln(-k - 8)

No solution 

400

Solve the equation-

log₄(b² + 11) = log₄(-10b + 2)

-9, -1 

500

Sophie is buying a used car for $4,500.00. The car is depreciating at a rate of 5% each month

a) Write an equation which models the value of the car after "x" months. 

b) How much will the car be worth after 8 months?

c) When will the car's value be $2,000?

a) y = 4500 × 0.95^x 

b) $2,985.39 

c) 15.81 months