The graph of g(x) shown below resembles the graph of f(x) 2^x, but it has been reflected over the x-axis. which is the equation of g(x)?

C.

Step-by-step explanation:

We know that the parent function is .

Now, the function that the graph shows intercepts , and the problem states that is the reflection of across the x-axis. That means the original function has to intercept , which is the reflected interception of .

We also know that y-interceptions are shown as independent terms, so the function is defined as follows

Where represent the y-interception.

The graph of is attached. The red curve represents and the blue curve represents . You can observe that models exactly the function we are looking for.

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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