Direct/Inverse Variations
Discontinuity
Simplifying Rational Expressions
Asymptotes
Multiplying and Dividing Rational Expressions
100

What kind of variation is the x,y graph?

X| 3   1.5   0.5    0.3

Y| 5    10    30    50

Direct: y=kx   Inverse: xy=k   

Neither: None of the numbers agree



What is Inverse Variation

100

Find ONLY the points of discontinuity in the equation

 (x2+2x)/(x2+2)= ? 


No points of Discontinuity

100

Simplify each rational expression + state any restrictions on the Variables.

2y/y2 + 6y =?

Restrictions:          

y≠0        

y≠-6

Simplified: 2/y + 6

 

100

Horizontal Asymptotes:


A. What is “y” when m<n

B. What is “y” when m>n 

C. what is ”y” when m=n

A. What is y=0

B. What is no horizontal asymptote 

C. What is y= a /b

100

What is the common phrase used when dividing rational expressions?

What is KEEP CHANGE FLIP.

200

What kind of variation is the x,y graph?

X| 3   4   7   9

Y| 5   6   8   10

Direct: y=kx   Inverse: xy=k   

Neither: None of the numbers agree

What is Neither (You do not get a common K)

200

Find ONLY the points of discontinuity in the equation

 (x-1)/(x+1)2= ? 

Points of discontinuity are at 

x= -1

200

Simplify each rational expression + state any restrictions on the Variables.

3y2 _ 3 / y2 _ 1=?

Restrictions:

y≠1

y≠-1

simplified: 3 

200

Find all Vertical Asymptotes:


y= x+1 /(x_2)(x_3)

Vertical Asymptotes at x=2 and x=3

200

Multiply these expressions and state any restrictions on the variables.


2x+4 /10x . 15x2 /x+2

Simplified: 

3x

Restrictions: 

x≠-2, x≠0

300

What kind of variation is the x,y graph?

X| 1    2      5     7

Y| 6    12    30    42

Direct: y=kx   Inverse: xy=k   

Neither: None of the numbers agree

What is Direct Variation 

300

What is a point of discontinuity? What are the two different types of discontinuity points?  

What is - Any value for x to make the denominator equal to 0.

what is - A removable discontinuity and a non-removable discontinuity. 

300

Simplify each rational expression + state any restrictions on the Variables.

w2+9w+18=?

Restrictions:

y≠-3

y≠4

Simplified: w+6/w-4 

300

Find the Horizontal Asymptote:


y=x_2 /x2_2x_3

Horizontal Asymptote at y=0

300

Divide these expressions and state any restrictions on the variables.

(5y /2x2) / (5y2 / 8x2)

Simplified: 

4 /y

Restrictions:

x≠0, y≠0

400

Suppose x and y vary inversely, and x=6 and y=9. What function models this inverse variation?


K= 6 x 9 = 54

this means

Y= 54/x

400

Find ONLY the points of discontinuity in the equation

 (x2 - x - 2)/(3x2 - 7x + 2)= ? 

Points of discontinuity are at 

x=1/3

x=2

400

Simplify each rational expression + state any restrictions on the Variables.

x2 + 13x + 40/ x2 _ 2x _ 35=?

Restrictions:

x≠-5

x≠7

simplified: x+8 /x_7

400

What is the Horizontal Asymptote 


y=x2 /2x_5

No Horizontal Asymptote, m>n 

400

Divide these expressions and state any restrictions on the variables.


(y2_5y+4 /y2_1) / (y2_9 /y2+5y+4)

Simplified:

(y_4)(y+4) /(y_3)(y+3)

restrictions:

x≠1, x≠-1, x≠-4, x≠-3, x≠3 

500

The force “F“ of gravity on a rocket directly with its mass m and inversely with the square of its distance “d” from Earth. Write a model for this combined variation. Write an equation to find the mass of the rocket in terms of F and d. 

Varied Directly means “n” multiplied by K

Varies Inversely means K/“n” 

Equation -- F= Km/d2 

500

Find ONLY the points of discontinuity in the equation

 (x3+3x2+2x)/(x3-1)= ? 

Points of discontinuity are at 

x=0

x=1

x=-1

500

Simplify each rational expression + state any restrictions on the Variables.


x2_7x+10 /x2_8x+15=?

Restrictions:

x≠5

x≠3

simplified: x_2 /x_3

500

Find all vertical asymptotes: 


x2+7x+12 /x2_2x_24

Vertical Asymptotes at x=6, x=-4 is NOT A V.A


P.S; A removable point of discontinuity is NOT a vertical asymptote 

500

Multiply these expressions and state any restrictions on the variables.

(y2_2y /y2+7y_18) . (y2_81 /y2_11y+18)

Simplified: 

y /y_2

restrictions: 

x≠-9

x≠9

x≠2

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