Posted by Casey on Tuesday, January 10, 2012 at 9:45pm.
Write an equation for rational function with given properties.
a) a hole at x = 1
b) a vertical asymptote anywhere and a horizontal asymptote along the x-axis
c) a hole at x = -2 and a vertical asymptote at x = 1
d) a vertical asymptote at x = -1 and a horizontal asymptote at y =2
e) an oblique asymptote, but no vertical asymptote
- Precalculus - Steve, Wednesday, January 11, 2012 at 12:30am
a) must have (x-1) in numerator and denominator
y = (x-2)(x-1)/(x-1) = (x^2 - 3x + 1)/(x-1)
b) must have (x-k) in the denominator, and not in the numerator. degree of numerator must be less than the degree of the denominator.
y = 12(x+3)/(x-5)(x+9)
c) must have (x+2) top and bottom, and have (x-1) in the bottom
y = 3(x+5)(x+2)/(x-1)(x+2) = (3x^2 + 21x + 18)/(x^2 + x - 2)
d) must have (x+1) in the bottom and have degree of top and bottom equal, with a factor of two up top.
y = (2x-5)/(x+1)
e) top degree must be bottom degree + 1
y = 3x^3/(x^2+3)
note the bottom is never 0.
- Precalculus - PS - Steve, Wednesday, January 11, 2012 at 12:34am
a) should read (x^2 - 3x + 2)/(x-1)
c) should read (3x^2 + 21x + 30)/(x^2 + x - 2)
Answer this Question
More Related Questions
- Pre-Calculus - Rational Functions does the following function have a hole or a ...
- advance functions gr12 - write an equation for a rational function whose graph ...
- math - Describe the vertical asymptote(s) and hole(s) for the graph of .y=(x-3)(...
- Algebra - Help! - Given the function: f(x)=(x^2+6x+5)/(x^2+3x−10) Find the...
- Rational Functions - Write an equation for a rational function whose graph has ...
- Math - Analyze the function algebraically. List its vertical asymptotes, holes, ...
- ****college algebra…radical functions**** - Create a rational function such that...
- college algebra - Given the following rational function, find a. the horizontal ...
- Algebra - functions - Given the function: f(x) = 5/(x-1)^2 Find the Horizontal ...
- College Algebra - Given the following rational functions,find:a.)the horizontal ...