Samuel Broom's Algebra III Fifth Block Jeopardy Extravaganza

The Other Topics Category™

100

Determine the end behavior of the following function:

f(x) = x² + 4x - 2

If x → (-∞), y → ∞

If x → ∞, y → ∞

200

In order, describe the necessary transformations to make function f(x) become function g(x).

f(x) = x³

g(x) = (x + 2)³ - 1

left 2, down 1

300

In order, describe the necessary transformations to make function f(x) become function g(x).

f(x) = |x|

g(x) = -|3(x + 1)| + 3

left 1, flip over the x-axis, vertical stretch by a factor of 3, up 3

500

In order, describe the necessary transformations to make function f(x) become function g(x).

f(x) = |x|

g(x) = -3|x + 3| - 3

left 3, flip over the x-axis, vertical stretch by a factor of 3, down 3

1000

f(x) = x⁴ + 2x³

For the function above:

a) State the maximum number of turning points that its graph could contain.

b) Determine all its real solutions.

c) State the multiplicity of any real repeated solutions. If the multiplicity of each solution is 1, then write "N/A".

d) Determine whether each x-intercept crosses or bounces off the x-axis.

a) 3

b) -2, 0

c) N/A

d) -2 → cross; 0 → cross

Inequalities

100

Solve. Write your answer in interval notation.

(x - 2)(x + 8) > 0

(-∞, -8) U (2, ∞)

200

Solve. Write your answer in interval notation.

(x - 7)(x + 5) > 0

(-∞, -5) U (7, ∞)

300

Solve. Write your answer in interval notation.

-x² + 3x + 18 > 0

(-3, 6)

500

Solve. Write your answer in interval notation.

x² + 2x - 3 > 0

(-∞, -3] U [1, ∞)

1000

Solve. Write your answer in interval notation.

(x³ - 343)(x⁴ - 2401) > 0

[-7, ∞)

Composite Functions

100

f(x) = -x - 1

g(x) = x³ - 5

Using the functions above, solve the expression below:

(f + g)(x)

x³ - x - 6

200

f(x) = -x - 1

g(x) = -2x

Using the functions above, solve the expression below:

g(f(0))

What is 2?

300

f(x) = x² - 3x

g(x) = 2x - 4

Using the functions above, solve the expression below:

(f · g)(-2)

What is -80?

500

f(x) = 4x - 2

g(x) = -x

Using the functions above, solve the expression below:

f(-x) · g(-x)

-4x² - 2x

1000

f(x) = 2x + 2

g(x) = 3x + 1

Using the functions above, solve the expression below:

(f ∘ g)(x²)

6x² + 4

Inverse Functions

100

Determine if the following functions are inverse:

f(x) = ⁴/₅x + 3

g(x) = ⁵/₄x - ¹⁵/₄

These two functions are inverse.

200

In terms of g(x), determine the inverse of the following function:

f(x) = √(x - 5) + 3

(No domain or range restrictions are required in your answer.)

g(x) = (x - 3)² + 5

300

In terms of g(x), determine the inverse of the following function.

f(x) = ∛[(-x + 2) / 2]

g(x) = -2x³ + 2

500

In terms of g(x), determine the inverse of the following function.

f(x) = -²/_x + 1

g(x) = 1 / [(-x + 1) / 2]

Alternate Answer: g(x) = [(-x + 1) / 2]^-1

1000

In terms of g(x), determine the inverse of the following function.

f(x) = ³/_{(x + 1)} + 2

g(x) = {1 / [(x - 2) / 3]} - 1

Alternate Answer: g(x) = [(x - 2) / 3]^-1 - 1

Random Questions That Will Make You Feel Pain™

100

Solve.

0⁰

What is undefined?

(Similar answers are allowed. Similarity is determined by Mr. Broom.)

200

If a function's degree is odd and its leading coefficient is negative, then what is the function's end behavior?

If x → (-∞), y → ∞

If x → ∞, y → (-∞)

300

Which Elijah is better?

What is Bergmann?

Alternate Answer: What is Elijah Bergmann?

500

Fill in the blank.

Elijah ____

What is Rock?

Alternate Answer: What is Elijah Rock?

1000

Write down Pascal's Triangle until the numbers on both ends of the triangle closest to the 1s are 7.

(If no one on your team was in Mrs. Hopkins' class last school year, this question is immediately passed to another team.)

Elijah Fredericks will verify your team's answer.