Rationals

Graphs

100

What is the equation of the parent graph for rationals

f(x)=1/x

200

Label the steps of how to tell if a function is continuous

1. f(c) must be defined. The function must exist at an x value (c), which means you can't have a hole in the function (such as a 0 in the denominator).
2. The limit of the function as x approaches the value c must exist.
3. The function's value at c and the limit as x approaches c must be the same.

300

In a rational graph, how do you find the Vertical Asymptote?

1. Simplify the rational expression

2. Set the denominator so it equals zero

3. Solve for x

400

How do you find a Slant asymptote on a graph

1. Only happens when no horizontal asymptotes 

2. Divide the numerator by the denominator using either long division or synthetic division

500

How do you find a hole of a rational graph?

1. Set anything you factor out when simplifying equal to zero.

2. Plug that value into the simplified version to get the y-value

Expressions

100

Solve: x^2-3x-10/x^2-4x+4 divided by x-5/x^2-2x

x(x+2)/x-2

200

Solve: 3*a^2/9*a*b

a/3*b

300

Solve: 3(a+b)/2(a+b)

3/2

400

12x^2 y-18xy^2/12x^2 y-8x^3

-3y/2x

500

Solve: (x+2) (x-1)/-(x+3)(x-1)

-x+2/x+3

Aysmptotes

100

what is the V.A. of y=2x-1/x-7

The vertical Asymptote is y=7

200

Find the H.A. for the eqaution y=x^2+5x/x^2+7x+10

y=1

300

Find the V.A. for the equation y=x^2-7x+12/x^2-9

x=-3

400

What is the H.A. for the equation y=2x^2+5x-3/x+3

There is no Horizontal Asymptote

500

what is the vertical asymptote of the equation: f(x)=1/x-3

x=3

Holes

100

In a equation represented by: y=x+2/(x+3)(x-4) what are the holes? if there are any

There are no holes in the equation

200

what is the hole in the equation: F(x)=(x+2)(x-2)/(x-3)(x+2)?

(-2,4/5)

300

what is the hole of: y=x-2/(x-2)(x-1)

Hole: x-2=0

x=2

400

what's the hole for the equation: y=2x/x^2-1 

There are no Holes.

500

What is the hole for the equation: f(x)=(x+4)(x-1)/(x-2)(x+4)

The hole is (-4,5/6)

Functions

100

What are the x and y intercepts for the equation: y=2x-1/x-7

y2=x

y=y7

200

what is the x and y intercepts for the equation: y=x^2+5x/x^2+7x+10

x=(0,0)

y=(0,0)

300

find the domain of y=x^2+5x/x^2+7x+10

(All real numbers)  x≠-2 and x≠-5

400

What's the range for y=2x^2+5x-3/x+3

(All real numbers)  y≠-7

500

What is the Domain for y=2x-1/x-7

(all real numbers) x≠7