Alex Trybek

5.1

100

Does the following function have a minimum or maximum?

f(x) = -2x² - 6x + 12

Maximum 

200

Determine the domain and range of the following quadratic function in interval notation.
f(x) = -2(x + 6)² + 2

Domain: (-oo,oo)

Range: (-oo, 2]

300

Determine the domain and range of the following quadratic function in interval notation.
f(x) = 2x² + 8x + 9

Domain : (-oo ,oo)

Range : [1, oo)

400

Use the vertex of the graph of the quadratic function and the direction the graph opens to find the domain and range of the function.
Vertex ( -4, 10), opens down

Domain: (-oo, oo)

Range (-oo, 10]

500

Write the equation for the quadratic function that contains the given point and has the same shape as the given function.
Contains ( -2, -1) and has the same shape as 2x². Vertex has x- coordinate of -1 

g(x) = 2 (x +1)² - 3

5.2

100

Identify the function as a power function, a polynomial function, or neither.
f(x) = 5x(x + 5)(x - 5)²

Polynomial function

200

Find the degree and leading coefficient for the given polynomial.
f(x) = -10x² - 7x⁵ + x - 10

Degree: 5

Leading Coefficient: - 7

300

Determine the end behavior for the function

f(x) = 5x⁴ +2x² + x - 5

As x -> oo, f(x) = 

As x -> - oo, f(x) = 

oo

oo

400

Find the intercepts for the functions

g(x) = 2(x + 4)(x + 3)(x - 1)

y intercept: (0, -24)

x intercept: (-4, 0), (-3, 0), (1, 0)

500

Use the information about the graph of a polynomial function to determine the function. Assume the leading coefficient is -1 or 1 

Y intercept is ( 0 , 4)

X intercept is ( -2, 0) (2, 0)

Degree is 2

As x -> -oo, f(x) -> -oo

As x -> oo, f(x) -> oo

-x² + 4 = f(x)

5.3

100

Find the x- intercepts of the polynomial

f(x) = x⁴ + x²

x intercepts: (-1, 0), (0,0), (1,0)

200

Find the zeros and give the multiplicity of each. List the zeros in order from least to greatest.
f(x) = x⁴(x - 4)³(x + 2)² 

Zero at -2; multiplicity of 2

Zero at 0; multiplicity of 4

Zero at 4; multiplicity of 3 

300

Find the zeros and give the multiplicity of each. List the zeros in order from least to greatest.

f(x) = 2x⁵ + 8x⁴ + 8x³ 

Zero at -2; multiplicity of 2 

Zero at 0; multiplicity of 3 

400

Find the zeros and give the multiplicity of each. List the zeros in order from least to greatest.

f(x) = (3x + 1)³ (x² - 6x + 9)

Zero at -1/3; multiplicity of 3

Zero at 3; multiplicity of 2

500

Use the given information about the polynomial graph to write the equation.

Degree 5. Roots of multiplicity 2 at x = -5 and x = 4, and a root of multiplicity 1 at x = 2. y intercept at ( 0, - 2) 

f(x) = 1/400 (x + 5) ² (x - 4)² (x - 2) 

5.4

100

Find the domain of the rational function 

f(x) = (x - 3)/(x + 4)

Domain {x | x ≠ __ } 

x ≠ -4 

200

Find the horizontal asymptote at 

f(x) = x/ x² - 9

y = 0

300

Find the x - and y- intercepts of the function 

f(x) = (x - 5)/(x² + 2)

x intercept : ( 5, 0)

y intercept : ( 0 , -5/2)

400

Write an equation for a rational function with the given characteristics 

Vertical asymptotes at x = -3 and x = 5

x - intercepts at ( - 2, 0) and (4, 0) 

y intercept at ( 0 , 8)

f(x) = 15 ( x + 2 ) ( x - 4) / (x + 3) (x - 5)

500

Identify the removable discontinuity 

f(x) = (x² + 9x + 20)/ (x + 5)

x - - 5 

Potpurri

100

Simplify the expression without using fractional exponents

a^7/2√32 - a^7/2√8

2a³√2a

200

Solve the quadratic equation by using the quadratic formula

2x² - 5x - 12 = 0

x = -3/2, 4

300

Find the domain of the function using interval notation

f(x) = 10/√x+7

Domain ( - 7, oo)

400

The startup cost for a restaurant is $130000 and each meal costs $15 for the restaurant to make. If each meal is then sold for $25, after how many meals does the restaurant break even?

x = 13000 meals 

500

Reduce the rational expression to lowest terms

(20a + 8b) / (4a² + 4ab)

(5a + 2b)/ (a² + ab)