Vertical Asymptotes of Rational Functions

Where is the vertical asymptote(s)?

-1

Identify the excluded value(s) of the rational expression. x^2 + 2x - 3/x^2 + 5x +6

-2 and -3

Find the dicontinuities of the function.f(x) = x2 + 12x + 27x2 + 4x + 3.There is a removable discontinuity at

-3,-3

What is the excluded value?

-4

Use the expression x - 6/ x + 4 How many excluded value(s) are there?

1

What are the vertical asymptotes of f(x)= 10/x^2 - 1

1, -1

Given x = wavelength and y = frequency are inversely related, solve for the constant for the given type of radiation. Gamma-Rays Frequency = 40 Hz Wavelength = 300,000

12,000,000

The equation that models the relationship between the wavelength and frequency of yellow light is:

302,400

Identify the vertical asymptote and the hole on the graph of the function f(x) = x2 + x − 6x2 − 6x + 8. There is an asymptote at x = . There is a hole at (, ).

4 2, -2.5

Identify the vertical asymptote of the function. f(x)= x^2 + 1/ 3(x-8)

8

What is the domain of the function?

All real numbers x, except x = 0

Complete the table of the values for the function f(x)= 1/x

a= -1 b= -10 c= -100 d= -1000 e= 1000 f= 100 g= 10 h= 1

Wavelength varies inversely with frequency. Let k be the product of wavelength and frequency. Complete the table using the inverse variation relationship.

a= 670 b= 600 c= 560

Simplify the rational expressions. x^2 - 16/ x^2 + 6x + 8 x^2 - x - 6 / x^2 - 3x - 10

c b

What happens as x approaches zero from the positive direction?

f(x) gets larger

What happens as x approaches zero from the negative direction?

f(x) gets larger in the negative direction