Unit 8 Wrap Up

Asymptotes

100

Find the vertical asymptote of 

f(x)=(3x+1)/(x+4)

x=-4

200

Determine the horizontal asymptote of 

f(x)=(2x+7)/(x-1)

y=2

300

Find the vertical asymptote(s) of 

(x-5)/(x^2-25)

x=-5

400

Find the horizontal asymptote of 

f(x)=(6x^2+5)/(2x^2-1)

y=3

500

Find the horizontal asymptote of 

f(x)=(4x^2-10)/(x+4)^2

y=4

Transformations of 1/x

100

Shift left 3

1/(x+3

200

Shift down 3

1/x-3

300

Reflect across the x axis

-1/x

400

Shift right 3 and up 2

1/(x-3)+2

500

Reflect and shift left 4 and up 2

-1/(x+4)+2

End Behavior

100

if x->infty then  y -> ? for

f(x)=x^2

infty

200

if x->-infty then  y -> ? for

f(x)=x^3

-infty

300

if x->infty then  y -> ? for

f(x)=(6x^2+5)/(2x^2-1)

3

400

if x->-infty then  y -> ? for

f(x)=(4x^2-10)/(x+4)^2

4

500

Write the equation of a rational function in the form  1/(x-h)+k that has  y->3  when 

x->infty

1/(x+some)+3

Direct and Inverse Variation

100

If y varies directly with x, what is the first step (general equation)?

y=kx

200

If y varies inversely with x, what is the first step (general equation)?

y=k/x

300

If y varies directly as x and y = 3 when x=12, find y when x = 10

y = 5/2

400

If V varies directly with the cube of h and inversely with t and V = 10 when h = 2 and t =4, what is the constant of variation? 

k = 5

500

If 1 triangle makes 8 cows and 2 triangles make 4 cows, what is the constant of variation and is it direct or inverse?

 k=8 inverse

Domain and Range

100

Domain and Range are always written from {blank} to greatest

LEAST

200

What is the domain of linear, quadratic, and cubic functions?

All real numbers

300

What is the domain of (middle school way)

-3/x+2

x!=0

400

What is the range of the function (written both ways)

-2/(x+3)-1

(-infty, -1)  \cup  (-1, infty)

y!=-1

500

Write an equation that has the following Domain 

(-infty, 2) \cup (2,infty)

a/(x-2)+k