Question

Task 3—Graphing Rational Functions Create a rational function with a linear binomial in both the numerator and denominator.

Answer 1

Construct a simple function f(x) = (x+1) / (x-1);

Vertical asymptote: setting the denominator to 0 we get
x - 1 = 0 => x = -1

Horizontal asymptote: since the numerator and denominator have the same degree, simply divide the coefficients of the highest terms, which is 1, implies there's a asymptote at y = 1;

x-intersection: set f(x) to 0 => f(x) = 0 => x = -1;

y-intersection: set x to 0 => f(0) = -1 / 1 = -1;