On a coordinate plane, a curved line, labeled f of x, with a minimum value of (negative 1.9, negative 5.7) and a maximum value of (0, 2) crosses the x-axis at (negative 2.5, 0), (negative 0.75, 0), and (0.75, 0), and crosses the y-axis at (0, 2). Which statement is true about the graphed function f(x)?

F(x) < 0 over the intervals (–∞, –2.5) and (–0.75, 0.75).
F(x) > 0 over the intervals (–∞, –2.5) and (–0.75, 0.75).
F(x) < 0 over the intervals ( –2.5, –0.75) and (–0.75, ∞).
F(x) > 0 over the intervals ( –2.5, –0.75) and (0.75, ∞)

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step-by-step explanation:

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

step-by-step explanation: