Inverse Variation
If x and y vary inversely, as x decreases, what happens to the value of y?
y - decreases
If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator,
What is a point of discontinuity?
When the numerator and the denominator have a common factor it crosses out creating a point of discontinuity
what is 42=16 in Logarithmic form
What is log416=2
Transformation between Log(x) and Log(X-4)
Translated 4 units Right
determine what variable is the x values and what variable is the y values.
The cost (c) per person of renting a private resort varies inversely as the number (n) of persons sharing the rent
n = x values
c = y values
If the degree of the numerator is bigger than the denominator,
then there is no horizontal asymptote
What is a vertical asymptote and what is an exception to having a vertical asymptote?
A vertical asymptote is when the denominator equals zero. If there is a hole (point of discontinuity) at a certain point then the asymptote does not exist.
solve
6x=216
x=3
Transformation between Log(x) and Log(x) + 2
What is Translated 2 units up
A hotel has enough food for 125 people for 16 days. If the number of people varies inversely as the number of days, how long will the food last if 75 more people join them?
10 days
If the degrees of the numerator and denominator are the same,
then divide the leading coefficients
Find the vertical asymptote. y= x2+2x-3/x2-5x-6
VA= x=-1 and x=5
solve
log2(6x−15)=log2(41−2x)
x=7
Transformation between Log(x) and -4Log(x)
Reflected and stretched by 4
Find the missing variable in this inverse variation (3/4,y) and (2/3,18)
y = 16
x3+3/x-1
no horizontal asymptote
Find the hole. y=x2-3x-10/x2+x-2
Hole= -2 because the numerator and denominator have x+2 in common
log(x)+log(x−15)=2
x =20
Transformation between Log(x) and 0.5Log (X + 5) + 1
What is compressed by 0.5, translated left 5 units and up 1 unit
Is xy = 13 a inverse equation?
yes
(x2+16x+64)/(3x+2)(x-1)
y = 1/3
find the VA, HA, and the hole. f(x)=x2+2x/-4x+8
VA= 2 HA= None Hole= None
If Janet gets a job that pays $25,000 and her pay goes up 3% a year. What will her pay be after one decade?
What is $33,597.91
Transformation between Log (X) and Log (X + F) - L
What is translated down L units and left F units