Answer:
a) What is the vertical intercept of f?
To find the vertical intercept of f, we need to set x equal to 0 and solve for y. We get y = -10, so the vertical intercept is -10.
b) What are the roots of f?
To find the roots of f, we need to set f(x) equal to 0 and solve for x. However, when we do this, we get no real solutions, so there are no real roots.
c) What are the vertical asymptotes of f?
According to the definition, the vertical asymptotes of f are the values of x where the function approaches infinity or negative infinity. In this case, f has a vertical asymptote at x = -5, since as x approaches -5 from the left, the function approaches positive infinity, and as x approaches -5 from the right, the function approaches negative infinity.
d) What is the horizontal asymptote of f?
The horizontal asymptote of f is the value that y approaches as x approaches positive or negative infinity. In this case, as x approaches negative infinity, y approaches -4, and as x approaches positive infinity, y approaches 4. Therefore, the horizontal asymptote of f is y = 4 (or y = -4).