1 Determine if the following statements are true and give an

1. Determine if the following statements are true, and give an explanation or counterexample.

(a) The function f(x) = x 2 + 2x 3 x 1 has a vertical asymptote.

(b) If f(x) = p(x) q(x) is a rational function with p(a) = d(a) 6= 0 for some number, a, then f has a vertical asymptote of x = a.

(c) The end behavior of the function f(x) = 2x 3 1 3x 2 + 2 is a linear function.

(d) The zeros of a rational function can occur at the same points as its vertical asymptotes.

Solution

a) x^2 +2x - 3x -1

No vertical asymtote . false

b) Please recheck the text of the question

c) f(x) = 2x^3 - 13x^2 +2

odd degree polynomial with a positive leading coefficient.

The end behaviour is a cubic functions.

False It is not a linear funtion

d) The zeros of the polynomial are the points where graph intercepts the x axis.

False