Answer:
The function [tex]y=\frac{x^{2}-16 }{x+4}[/tex] simplifies to [tex]y=x-4[/tex] through factoring and division. Since [tex]y=x-4[/tex] is a linear function, this results in a line with y-intercept (0,-4) and slope 1.
Step-by-step explanation:
The rational function [tex]y=\frac{x^{2}-16 }{x+4}[/tex] can be simplified by factoring the numerator. The numerator is a difference of squares quadratic which factors as shown:
[tex]y=\frac{(x+4)(x-4) }{x+4}[/tex]
We can now divide (x+4) into the numerator which cancels out and leaves:
[tex]y=x-4[/tex]
To graph a linear line, we find the y-intercept -4 on the y-axis and plot the point. From that point we rise 1 and run 1 for a slope of 1. We connect the two points.
