Algebra 2!

Inverse Variation

100

If x and y vary inversely, as x decreases, what happens to the value of y?

y - decreases

200

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

300

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

400

Find the missing variable in this inverse variation (3/4,y) and (2/3,18)

y = 16

500

Is xy = 13 a inverse equation?

yes

Horizontal Asymptotes

100

If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator,

then the horizontal asymptote is y = 0

200

If the degree of the numerator is bigger than the denominator,

then there is no horizontal asymptote

300

If the degrees of the numerator and denominator are the same,

then divide the leading coefficients

400

x³+3/x-1

no horizontal asymptote

500

(x²+16x+64)/(3x+2)(x-1)

y = 1/3

Vertical Asymptotes & Holes

100

What is a point of discontinuity?

When the numerator and the denominator have a common factor it crosses out creating a point of discontinuity

200

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.

300

Find the vertical asymptote. y= x²+2x-3/x²-5x-6

VA= x=-1 and x=5

400

Find the hole. y=x²-3x-10/x²+x-2

Hole= -2 because the numerator and denominator have x+2 in common

500

find the VA, HA, and the hole. f(x)=x²+2x/-4x+8

VA= 2 HA= None Hole= None

Logarithms & exponentials

100

what is 4²=16 in Logarithmic form

What is log₄16=2

200

solve

6^x=216

x=3

300

solve

log₂(6x−15)=log₂(41−2x)

x=7

400

log(x)+log(x−15)=2

x =20

500

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

transformations

100

Transformation between Log(x) and Log(X-4)

Translated 4 units Right

200

Transformation between Log(x) and Log(x) + 2

What is Translated 2 units up

300

Transformation between Log(x) and -4Log(x)

Reflected and stretched by 4

400

Transformation between Log(x) and 0.5Log (X + 5) + 1

What is compressed by 0.5, translated left 5 units and up 1 unit

500

Transformation between Log (X) and Log (X + F) - L

What is translated down L units and left F units