For what values of x does the function shown in the graph below appear to negative? explain and only give an answer that’s correct !

Choice D) x < -2 and x > -1

Explanation:

Look at the curve where it is below the horizontal x axis. This is to the left of the vertical asymptote x = -2 and to the right of the vertical asymptote x = -1. So that's how I'm getting x < -2 and x > -1. Basically it's every x value but the stuff in between the vertical asymptotes. The vertical asymptotes themselves aren't counted as well, because the curve slowly approaches the asymptotes but never actually gets there.

side note: the portion of the curve on the interval -2 < x < -1 is above the x axis so this part is positive

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is