Snazzy Partial Fraction Decomposition
Graphing and Writing Gnarly Equations
Sassy Inverse Functions
Fancy Composition Equations
Fun Facts of Mclean HS!
100
Write the partial fraction decomposition of f(x)= (x+13)/(x²-x-20)
f(x)= 2/(x-5) + -1/(x+4)
100
Write the limit as x approaches negative and positive infinity of the equation f(x)= -5x^7+6x^4+8
lim(x→∞)f(x)=-∞ lim(x→-∞)f(x)=∞
100
Find the inverse function of the equation f(x)= (x-1)/(x+2)
f^-1(x) = (2x+1)/(1-x)
100
If f(x)= x^2+4x and h(x)= 3x-5, find (f-h)(x)
(f-h)(x)= x^2+x+5
100
Is there truly a pool on the roof?
NO.
200
Write the partial fraction decomposition of f(x)= (x²-3)/(x³+2x²+x)
f(x)= -3/x + 4/(x+1) + 2/(x+1)²
200
Write an equation with the real zeros of -5, 4 that also has a degree of 4.
f(x)= (x+5)(x-4)(x²+1)
200
Find the inverse of the equation f(x)= √(x-4)
f^-1(x)= x²+4
200
If f(x)= x^2+4x and h(x)= 3x-5, then what is (h/f)(x)
(h/f)(x)= (3x-5)/(x^2+4x)
200
Who is Mclean's Directer of Student Activities?
Mr. Jim Patrick
300
Write the partial fraction decomposition of f(x)= (-x²-22x-50)/(x³+10x²+25x)
f(x)= -2/x + 1/(x+5) + -7/(x+5)²
300
Graph the equation and give its turning point(s) and its domain and range. f(x)= -x³
Turning point= (0,0) Domain= ℝ Range= ℝ
300
Solve to see if these two equations are inverses f(x)= 6/(x-4) g(x)= 6/x +4
Yes, they are
300
If f(x)= x^2+1 and g(x)= x-4, then find [f o g](x)
[f o g](x)= x^2-8x+17
300
How many hallway colors are there?
5
400
Write the partial fraction decomposition of f(x)= (17x+256)/(x³-16x²+64x)
f(x)= 4/x + -4/(x-8) + 49/(x-8)²
400
Find all the zeros of the equation when two of the zeros are 2 and 1. f(x)= -3x^5 + 21x^4 - 45x³ + 45x² - 42x + 24
2, 1, 4, ±i
400
Find the inverse of the function and state any restrictions to its domain. f(x)= (6x+3)/(x-8)
f^-1(x)= (8x+3)/(x-6), x≠6
400
If f(x)= x^2-9 and g(x)= 1/(x+1) then what is [g o f](x)?
[g o f](x)= 1/(x^2-8)
400
What is Ms. Quarry's favorite team?
The Virginia Tech Hokies
500
Write the partial fraction decomposition of f(x)= (x^4-2x³+8x²-5x+16)/(x(x²+4)²)
f(x)= 1/x - 2/(x²+4) + 3/(x²+4)²
500
Graph and identify the domain, range, intercepts, if it's continuous (if so, specify), where it's increasing or decreasing, and limits as x approaches negative and positive infinity of the equation f(x)=3/4 x-³
Domain: (-∞, 0) U (0, ∞) Range: (-∞, 0) U (0, ∞) No intercepts Continuous: (-∞, 0) U (0, ∞) Decreasing: (0, ∞) Increasing: (-∞, 0) As x → ∞, f(x) → 0 As x → -∞, f(x) → 0
500
Show algebraically that f(x) and g(x) are inverse functions f(x)= -3x²+5 g(x)= √(5-x)/√(3)
f[g(x)]= -3(√(5-x)/√(3))² + 5 = (-3(5-x))/(3) + 5 = x-5+5= x; g[f(x)]= √(5-(-3x²+5))/√(3) = √(3x²)/√(3) = √(x²) = x
500
If f(x)= x^3-5x^2+72 and g(x)= 2x-43, then what is [f o g](x) AND [g o f](x)?
[f o g](x)= 8x^3-536x^2+10234x-70190 [g o f](x)= 2x^3-10x^2+101
500
Who is McLean named after?
John Roll McLean
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