Which is a valid prediction about the continuous function f(x)?
Х
-3
-2
-1
0
1
2
f(x)
-15
-5
0
5
0
-5
Of(x) < 0 over the interval (-00, ).
Of(x) > 0 over the interval (-1, oo).
Of(x) > 0 over the interval [-1, 1).
Of(x) < 0 over the interval (0, 2).

The valid  prediction about the continuous function f(x) is:

             f(x) ≥ 0 over the interval [5, ∞).

Step-by-step explanation:

The table for f(x) is given by:

                 x         f(x)

                 -5         8

                 -3         4

                 -1          0

                  1          -2

                  3         -2

                  5          0

                  7          4

From the table of values of the function f(x) we see that the value of the function f(x) first decreases and then attains it minimum ( i.e. -2) and then increases continuously after x=5.

            Hence, the correct answer is:

                f(x) ≥ 0 over the interval [5, ∞).

(

f(x) ≤ 0 over the interval [–1, ∞).

This option is incorrect since the value of the function at x=5 is greater than zero.

f(x) > 0 over the interval (–∞, 1).

At x= =-1 we have f(x)=0 .

Hence, the option is incorrect.

f(x) < 0 over the interval (–∞. –1).

At x= -5 the value of f(x) is greater than zero.

Hence, this option is incorrect   )

Reflectional symmetry is the mirror image of one side of image to the other when we divide the image. In other words it is one half of image is the reflection of other half of image.

In isosceles trapezoid, the length of the sides are same . the bases are not same.

When we draw a vertical line in the middle of  isosceles trapezoid, the left side of the image is the reflection of right side .

So there is only one line of reflection symmetry.