The graph f(x) shown below resembles the graph of g(x) = |x| but it has been flipped over the x axis which of the following is the equation of f(x)

f(x)=-|x|

Step-by-step explanation:

We have been given a graph of f(x) which resembles with the graph of function g(x) where g(x)=|x|.

It says that graph is flipped over the x-axis.

Now we have to find about which of the following choice correctly describes the given graph.

We know that |x| means absolute value of x so that means g(x)=|x| is absolute function in shape of V.

We know that flipping over x-axis can be done by changing f(x) into -f(x).

Hence correct answer is choice D) F(x)=-|x|

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

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