Graph all vertical and horizontal asymptotes of the rational function.
F(x)=-6x-13/-2x-7
To graph the vertical and horizontal asymptotes of the rational function:
F(x) = (-6x - 13) / (-2x - 7)
1. Vertical asymptote:
To find the vertical asymptote, set the denominator equal to 0 and solve for x:
-2x - 7 = 0
-2x = 7
x = -7/2
Therefore, the vertical asymptote is x = -7/2.
2. Horizontal asymptote:
To find the horizontal asymptote, compare the degrees of the numerator and the denominator. Since both are the same degree (1), divide the leading coefficient of the numerator by the leading coefficient of the denominator:
Horizontal asymptote = (-6) / (-2) = 3
Therefore, the horizontal asymptote is y = 3.
Graph of the function F(x) = (-6x - 13) / (-2x - 7):
- Graph the vertical asymptote x = -7/2 as a vertical dashed line.
- Graph the horizontal asymptote y = 3 as a horizontal dashed line.
- Plot the function curve approaching the asymptotes as x approaches negative and positive infinity.
Please note that the graph may also be sketched to illustrate the behavior of the function when approaching the asymptotes.