Find the domain and range of the rational function graphed b

Find the domain and range of the rational function graphed below. Find the horizontal and vertical of the national function graphed below. f(x) = 3x + 5/5x - 2

Solution

1st Graph:

f(x)    as x - 2 f (x) - as x -2, f(x) -3 as x , f(x) -3 as x -

Domain ( - , - 2) and ( - 2, ) Range is y -3 (( - , - 3)and (- 3,). The answer is A.

2nd Graph:

An asymptote is a line that the graph of a function approaches but never touches. Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function

The domain is all x-values other than the zeros of the denominator, and the vertical asymptotes are at the zeros of the denominator. The domain of a rational function consists of all real numbers x except those for which the denominator is zero.

Vertical Asymptotes are x = - 3 and x = 3 i.e x = ± 3 Horizontal Asymptote is y = -2

The answer is C.

12. B   5x -2 = 0 or, x = 2/5

13. x² -1 = 0 or x = ±1 B x = 1, x = -1