7.1 Inverse Variation
Give an example of a reciprocal.
x -> 1/x
1/x -> x
How do you find vertical asymptotes?
set denominator = 0 and solve for x
Give an example of a rational expression.
P(x)/Q(x)
When adding and subtracting rational expressions what must you check first?
Common denominators
What is it impossible for the graph of the function y=1/x to intersect the x-axis?
There is an asymptote at the x-axis because you cannot divide by zero, you get undefined.
How do you know you have an inverse variation?
-One variable increases other decreases
-has a common constant of variation
-y=k/x
-see "varies inversly"
How do you find horizontal asymptotes? Describe each.
case 1 N< D y=0
case 2 N> D y= none
case 3 N=D y= LC/LC
Rational expression is the mathematical phrase of saying:
Fraction
Explain in detail how to add or subtract rational expressions with uncommon denominators.
find common denominator by factoring and checking what each rational expression should be multiplied to the numerator and denominator, then combine like terms in numerator and simplify any factors.
Find the vertical and horizontal asymptote.
h(x)= x2 / (1x/4 + 1/8)
HA: none
VA: x= -0.5, -1/2
Give an example of a real world scenario of an inverse variation.
some phenomenon increases while the other decreases.
Given g(x)= 1/(x+2) - 6
What are the equations of the asymptotes?
x= -2
y= -6
Find the product: 4x2yz/ x * 3y2/ 16y4z
12x2y3z/ 16xy4z=
3x/4y
Find the sum:
x2 -3x + 10 / x2 - 49 + 2x -5 / (x-7)(x+7)
x2 - x + 5/ x2 - 49
x2 -x +5/ (x-7)(x+7)
Solve 1/(x+4) = 2
1= 2x +8
-7= 2x
x= -7/2= -3.5
What is the reciprocal function and what does it look like?
f(x)= 1/x and graph
Find the domain and range of g(x)= 12/(x-3) + 4
D: x| x is not 3
R: y| y is not 4
Simplify x3 - 5x2 - 24x / x(x2 + x - 72)
(x+3)/ x+9
Find the difference
3x/ 4y2 - y/ 10x
15x2/ 20xy2 - 2y3/ 20xy2
15x2 - 2y3 / 20xy2
Find the perimeter of the quadrilateral in the simplest form.
1/x + x + 2/3x + 2x
3/3x + 3x2/3x + 2/3x + 6x2/ 3x
9x2 + 5 / 3x
In an inverse variation, x= 12 and y= 3/4. What is the equation that represents the inverse variation? What is the value of x when y= 15
y= 9/x
x= 3/5
Find the vertical and horizontal asymptotes of
f(x)= 2x2 + x - 9 / x2 + 23x - 50
VA: x= -25 x= 2
HA: y= 2
Divide the rational expression
x3+3x2+3x+9/(x+1)(x-1) divided by x2+5x+4/x2+3x-4
x2(x+3) + 3(x+3)
(x2+3)(x+3)/ (x+1)(x-1) divided by (x+1)(x+4)/ (x+4)(x-1)
(x2+3)(x+3)/(x+1)(x-1) * (x+4)(x-1)/(x+1)(x+4)
(x2+3)(x+3)/ (x+1)2
Simplify (3x-5)/ (x2 - 25) - 2/(x+5)
(3x-5)/ (x+5)(x-5) - (2x-10)/(x+5)(x-5)
x+5/ (x+5)(x-5)
1/(x-5)
Simplify (2- (1/x)) / (x+(2/x))
2x/x - 1/x / x2/x + 2/x
(2x-1)/x / (x2 + 2)/x
(2x-1)/x * x/(x2 +2)
(2x-1)/(x2+2)