Question

What is the graph of the function f(x) = the quantity negative x squared plus x plus 20 over the quantity x plus 4?

A) a line that crosses the x axis at negative 5 and the y axis at 5. Discontinuity exists at negative 4, 1.
B) a line that crosses the x axis at 5 and the y axis at negative 5. Discontinuity exists at 4, negative 1.
C) a line that crosses the x axis at negative 5 and the y axis at negative 5. Discontinuity exists at negative 4, 9.
D) a line that crosses the x axis at negative 5 and the y axis at negative 5. Discontinuity exists at 4, negative 9.

Answer 1

For this case we have a function of the form:
f (x) = (-x ^ 2 + x + 20) / (x + 4)
Rewriting we have:
f (x) = (- (x + 4) (x-5)) / (x + 4)
f (x) = 5 - x
The equation is a straight line.
Cut with x: (5, 0)
Cut with x: (0, 5)
Discontinued at x = -4
f (-4) = 5 - (-4)
f (-4) = 5 + 4
f (-4) = 9
That is, discontinuous in:
(x, y) = (- 4, 9)
Answer:
a line that crosses the axis at positive 5 and the axis at positive 5. Discontinuity exists at negative 4, 9.
Note: check the function again or the options.