Polynomials
What do we get when a polynomial function touches or crosses the x-axis?
A solution
Simplify.
2^(4/3)
2root3(2)
Determine whether the function is an example of exponential growth or decay.
y=-80(.67)^x
Exponential Growth
Simplify.
(8x)/(x-2)-16/(x-2)
8
Corruption
All points deleted.
Simplify. Write in standard form.
(6x^2+7x-12+x^3)-(6x^2+4x-2x^4)
2x^4+x^3+3x-12
Solve for x.
sqrt(x-11)+9=13
x=27
Rewrite in exponential form.
log_3 81=4
3^4=81
Identify the horizontal asymptote (HA) of the function.
f(x)=(8x^2+7x-12)/(4x^2-5x+11)
y=2
Recession
Random team instantly loses 200 points.
Write an equation for a quintic trinomial that crosses the y-axis at 15 and has negative leading coefficient.
y=-ax^5+bx^n+15,n=4,3,2,1
Simplify.
sqrt(27)-sqrt(12)+sqrt(3)
2sqrt(3)
Solve for x. Check for extraneous solutions.
log_11x+log_11(x+12)=log_11 28
x=2
Identify the horizontal asymptote (HA) and vertical asymptote (VA) of the function.
f(x)=4/(x+4)-6
x=-4 and y=-6
Charity
Highest scoring team gives 300 points to the lowest team.
Solve the equation to find the zeros of the function and their multiplicities.
x^4+8x^3+16x^2=0
x=0,x=0,x=4,x=4
Simplify.
5/(2+sqrt(x^2))
(10-5sqrt(x^2))/(4-x^2)
Find the inverse function.
y=(log_2(3x))/3-2
y^-1=2^(3x+6)/3
Solve for x.
1/x+1/(x-3)=(x-2)/(x-3)
x=1
Economic Equality
Everyone’s points are evenly redistributed among all teams.
Determine the value of k so that the divisor is a factor of the dividend.
(3x^4-16x^3+kx^2-8x+7)÷(x-7)
k=-34
Simplify.
root(3)(27x^15y^3)
3x^5y
You invest $1500 into an account earning 5% interest compounded continuously. How much
money will be in the account after 10 years? Round to the nearest hundredth.
$2473.08
Identify the holes of the function.
(x^2-4)/(x^2-x-6)
x=-2
Lottery
Random team instantly gains 500 points.