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100
List all possible rational zeros of the function.
f(x)=5x^4-2x^2+7x-8
p/q=+-1,+-2,+-4,+-8,+-1/5,+-2/5,+-4/5,+-8/5
100
What is the formula that relates profit, cost, and revenue?
Profit = Revenue - Cost
P = R - C
100
Use synthetic division to determine if x=8 is a zero of the function f(x)=2x^3-25x^2+66x+48
Yes, the remainder is 0.
100
Simplify the expression. Write your answer in standard form.
(7+2i)(-3-i)
-19-13i
100
Find the x- and y-intercept(s) of the function.
f(x)=frac{x-4}{x-7}
x-int: (4,0)
y-int: (0,4/7)
200
Describe the end behavior of the function.
f(x)=-2(x+5)^4+2x^3-7x
x->-infty,f(x)->-infty
x->+infty,f(x)->-infty
200
Describe the end behavior of the function
f(x)=4x-1/2x^3
x->-infty,f(x)->+infty
x->+infty,f(x)->-infty
200
Find the maximum of the function
f(x)=70,000+110x-0.055x^2
frac{-b}{2a}=1000
f(1000)=125,000
200
Simplify the expression. Write your answer in standard form.
sqrt{-100}-2(6+3i)
-12+4i
200
Write the vertex form equation of the quadratic function with a vertex at (1, 2) and goes through (3, -6).
y=-2(x-1)^2+2
300
What is the complex conjugate of 10-sqrt{-25} ? Write your answer in standard form.
10+5i
300
Identify any vertical and horizontal asymptote(s) of the function.
f(x)=frac{8}{x^2-10x+24}
V.A.: x=4, x=6
H.A.: y=0
300
Use long division. Write your remainder as a fraction.
(30x^2-3x+8)div(5x-3)
6x+3+frac{17}{5x-3}
300
Simplify the expression. Write your answer in standard form.
frac{10}{7-2i}
70/53+20/53i
300
Solve the inequality. Write your answer in interval notation.
12x^2+5x<2
(-2/3,1/4)
400
Use your knowledge of transformations to sketch the function.
f(x)=-3(x+1)^2+5
Vertex @ (-1,5), upside down, vertical stretch
400
Identify the domain of the function.
f(x)=frac{x+5}{x^2-x-56}
Domain: (-infty,-7)cup(-7,8)cup(8,infty)
400
Factor the polynomial 2x^3+11x^2-21x-90 completely given x=-6 is one of its zeros.
(x+6)(2x+5)(x-3)
400
Find a cubic polynomial with zeros at 5 and 3i. Also the polynomial has the value f(0)=-15
f(x)=1/3(x^3-5x^2+9x-45)
=1/3x^3-5/3x^2+3x-15
400
Solve the inequality. Write your answer in interval notation.
frac{2}{x+1}geqfrac{3}{x-1}
(-infty,-5]cup(-1,1)
500
Write the function in vertex form.
f(x)=x^2-6x+11
f(x)=(x-3)^2+2
500
Identify the vertex and the exact x-intercepts of the function.
f(x)=(x+7)^2-19
Vertex: (-7, -19)
x-ints:
(sqrt19 -7,0) & (-sqrt19-7,0)
500
Write the polynomial in completely factored form.
x^4+5x^3+22x^2+80x+96
(x+3)(x+2)(x+4i)(x-4i)
500
Sketch the graph of the function. Include all asymptote(s) and intercept(s).
f(x)=frac{x}{x^2-16)
500
Sketch the graph of the function. Include all asymptote(s) and intercept(s).
f(x)=frac{6x^2-11x+3}{3x^2-x}
