To graph the rational function \(F(x) = \frac{-6}{-x-3}\), we first need to identify the vertical and horizontal asymptotes.
Vertical asymptote:
The vertical asymptote occurs where the denominator of the rational function is equal to zero. In this case, the vertical asymptote occurs at \(x = -3\).
Horizontal asymptote:
To determine the horizontal asymptote, we compare the degrees of the numerator and denominator. Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote occurs at \(y = 0\).
Now, let's plot two points on each piece of the graph:
For the left side of the vertical asymptote (\(x < -3\)):
Let's choose \(x = -4\) and \(x = -5\).
\(F(-4) = \frac{-6}{-(-4)-3} = \frac{-6}{1} = -6\)
\(F(-5) = \frac{-6}{-(-5)-3} = \frac{-6}{2} = -3\)
For the right side of the vertical asymptote (\(x > -3\)):
Let's choose \(x = -2\) and \(x = -1\).
\(F(-2) = \frac{-6}{-(-2)-3} = \frac{-6}{1} = -6\)
\(F(-1) = \frac{-6}{-(-1)-3} = \frac{-6}{2} = -3\)
Now, let's plot the points and graph the function.
Please wait while I generate the graph...
Graph the rational function
F(x)=-6/-x-3
Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-function button.
1 answer
1 answer