Direct and Inverse Variation
Find the Asymptote
Key Features of Rationals
Simplify The Rational
Solve The Rational
100
X and Y are directly related, and x=4 while y=10.  What is k?
K = 5/2
100
What is the vertical asymptote of the following reciprocal function:


y=2/(x-3) +4

x=3
100
What is the y-intercept of the following function:


y=(x^2-4)/(x+2)

y = -2
100
Simplify The Rational


(3x^3)/(12x^2+9x)

(x^2)/(4x+3)

100
Solve the rational:


3/2+1/x=2

2
200
X and Y are inversely related and y=6 while x=4.

What is k?

K=24
200
What is the horizontal asymptote of the following reciprocal function?


y=8/(x+3) - 3

y=-3
200
What is/are the x-intercept/s of the following function?


y=(x^2 -4)/(x+2)

x=2
200
Simplify The Rational


(4xy^3)/(x^2y) * (y)/(8x)

y^3/(2x^2)

200

3/(4x) = 5/(x+2)

6/17
300
Create the formula from the following: w varies directly with z and inversely with the square root of x.

w=(kz)/(sqrt(x))

300

What is/are the vertical asymptote/totes of the following rational function?

y=(x+5)/(x^2 -25)


The only vertical asymptote is at x=5.
300
What is the domain of the following function?


y=(x+4)/(x^2 - 16)

All real numbers except 4 and -4
300
Simplify The Rational


(32x^3y)/(y^9)-:(8x^4)/(y^6)

4/(xy^2)

300

8/(x+2)+8/2=5

6
400
z varies inversely with x-squared and directly with a and b.

z=(kab)/(x^2)

400
What is the horizontal asymptote of the following rational function?


y=(x^3 -1)/(x+4)

There is NO horizontal asymptote
400
What is the range of the following function:


y=(3x^2 + 2x - 8)/(2x^2 - 4)

All real numbers except 3/2
400
Simplify the rational


(2x^2 - 10)/(x+1)*(x+2)/(3x^2-15)

(2(x+2))/(3(x+1)

400

(-3)/(x+1)=4/(x-1)

-1/7
500
X and Y vary inversely.  When x = 4, y=10.  Find k and use it to find y when x = 20.  
y=2
500
What is the horizontal asymptote of the following function?


y=(6x^4 + 3x^2 -6)/(12x^4 -3x+2)

The horizontal asymptote is at y=1/2
500

How many vertical asymptotes does the following function have?

y=(x^2 +2x - 8)/(2x^2-4)

It has two vertical asymptotes.
500
Simplify the Rational


(x^2 - 14x + 48)/(x^2 - 6x)-:(3x-24)

1/(3x)

500
Solve the rational


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

7/2
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