Chapter 4(1st)

4.1

100

Define Constant Variation.

The ratio representing the relationship between x and y variables. 

200

What are the vertical and horizontal asymptotes of the equation 

g(x)= 1/(x-2) +4

X=2 

Y=4

300

x- |  1   |     2    |   3  |   5  |    6   |  15 |

y- |25.5 | 12.75 | 8.5 |  5.1 | 4.25 | 1.7 |

Is this an example of an inverse variation?

Yes, since the product is consistent and equals 25.5

400

An inverse variation, X=2 when Y=10. Write an equation to represent the inverse variation given the equation y=k/x. Then find the value of x when y=5.

K=20

X=4 and Y=5

500

In inverse variation, X=10 when y=3. Write an equation to represent the inverse variation given the equation y=k/x. Then find the value of y when x=-2.

y=30/x or k=30

x=-6 and y=-5

4.2

100

Define Asymptope. 

The line that approaches a given line but does not approach it at a finite distance. 

200

What are the vertical asymptotes for the graph of f(x)=(3x-2)/(x²+7x+12)?

x=-3, -4

300

What is the horizontal asymptote of the function f(x)=(ax²+bx+c)/(dx²+ex+f)?

a/d

400

Write a function that has vertical asymptotes at x=-3 and x=1, and a horizontal asymptote at y=3.

(3x²)/(x²+2-3)

500

The rate of how fast a snail moves is shown by the function f(x)=(0.5x)/(x²-1), where x is the time in minutes since it started moving. How far has the snail moved after 4 minutes, in meters?

0.13 meters. 

4.3

100

Define Simplified Form of a Rational Expression. 

What makes a rational expression considered simplified. 

200

Whats the domain of ( y²-5y-24 ) / ( y²+3y+2 )?

y does not equal -1 or -2

300

Simplify the expression: (2x²+11x+5) / (3x²+17x+10)

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

400

Whats the quotient of 

( 9-x² ) / ( 3x ) and ( x²+6x+9 ) / ( 3x )?

-( x-3 ) / ( x+3 )

500

The area of a rectangle is ( x²-4 ) / ( 2x )in², and its length is ( x+2 )² / ( 2 )in. What is the width of the rectangle?

( x-2 ) / ( x( x+2 ))in

4.4

100

Define Distribution Property.

The property that lets you multiply a sum of at least 2 attends that will give the same result as multiplying each addend individually. 

200

Find the LCM. x²-y² and x²-2xy+y²

(x+y)(x-y)²

300

Jake adds 5x+6/x+3 + 3x-4/2x = 8x+2/3x+3. What's the error and correct sum?

Jake added the numerator and denominator instead of finding the LCD. Correct answer is 13x²+17x-12/2x(x+3)

400

Find the difference 2/n+4 - n²/n²-16

2-n/n-4

500

Find the sum of x+3/x²-1 + 2/x²-3x+2

x+4/(x+1)(x-2)

4.5

100

Define Rational Equation. 

An equation containing at least one fraction. 

200

find the extraneous solution for x^2+4/x-1=5/x-1

1 

300

solve 3/x-3=x/x-3 - x/4

x=-4

400

Arthur and Cheyenne can paint a wall in 6 hours when working together. Cheyenne works twice as fast as Arthur. How long would it take Cheyenne to paint the wall by herself? What is the value of x?

x=18, 9 hours

500

Solve x/1 + 6/x-3 = 2x/x-3

x=2