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Adding and Subtracting Rational Expressions and Polynomials
Multiplying and Factoring Polynomials
Exploring Graphs of Rational Functions
Simplfying Rational Polynomials
Multiplying and Dividing rational Expressions
100
Simplify (2a+4c+8) + (7a-9c-3)
9a-5c+5
100
(x-6)(2x+5)
2x²-7x-30
100
What determines where a rational function has a hole?
When they occur at restricted values that result from a factor of the denominator that is also a factor of the numerator
100
8x^2w + 10w / 8xw
4x2 + 5 / 4x
100
2/3 x 5/8
5/12
200
(1/2x + 1/3y) – (1/5x-y)
3/10x + 4/3y
200
2x(3x-5x²+4y)
6x²-10x3+8xy
200
What determines where a rational function has a vertical asymptote?
When they occur at restricted values that are still zeros of the denominator after simplification
200
n^3 - m^2n / n^2 + mn
n - m
200
Simplify and state any restrictions: (x+1)(x-3)/(x+2)^2 x 2(x+2)/(x-3)(x+3)
2(x+1)/(x+2)(x+3) restrictions x does not equal -3,-2, and 3
300
n/m+m/n-m
n^2+m^2-m^2n/mn
300
ac + bc +ad + bd
(a + b)(c + d)
300
When does a rational function have the horizontal asymptote at y=0?
When its X value = 0
300
2u^3v + u^2v^2 / 4u^4v - u^2v^3
1 / 2u - v
300
Simplify and state the restrictions: 15m^2+mn-2n^2/2n-14m x 7m^2-8mn+n^2/5m^2+7mn+2n^2
-(3m-n)(m-n)/2(m+n) Restrictions m does not equal to 1/7n,-2/5n and -n
400
5y/3-y/2
7y/6
400
15y^3 + 26y^2+7y
y(3y+1)(5y+7)
400
When does a rational function have another(not y=0) as a horizontal asymptote?
When the X value causes the denominator to be 0
400
3p^3 - 3ps^2 / 3p^2s
(p + s)(p - s) / ps
400
Simplify and state the restrictions 2(x+1)/3 X x-1/6(x+1)
(x-1)/9 Restrictions x does not equal to -1
500
Determine wheter these two equations are equivalent: F(X) =(2x²+7x-2) – (3x+7) and G(X)=(x²+12)+(x²+4x-17)
these two equations are not equivalent as they give two different answers
500
(5x + 2y)2 - 5x - 2y
(5x + 2y)(5x + 2y - 1)
500
Simplify the following function and state the restrictions: f(x)= x2-4/x-2
x+2 restrictions x does not equal 2 2 is also a hole
500
6xy + 2y / 3xy + 3x + y + 1
2y / y + 1
500
Simplify and state the restrictions: x^2-5xy+4y^2/x^2+3xy-28y^2 X x^2+2xy+y^2/x^2-y^2
x+y/x+7y Restrictions x does not equal -y,-7y,y, and 4y