The graph of f(x)=1/x
has been transformed to create the graph of g() = 1/x-h.

D, h = -2

Step-by-step explanation:

This is a horizontal shift, the general case is:

If you have a function f(x), the function g(x) = f(x - A) wil move the graph of f(x) A units to the right (Where A is a positive number).

And h(x) = f(x + A) will move the graph A units to the left.

in this case, we have:

g(x) = f(x - h) = 1/(x - h)

Then to find the value of h, we need to count how many units the graph of f(x) has been moved.

We can see that the asympthotes are at x = -2, and those would be at x = 0 for f(x) = 1/x.

Then we have a horizontal shift of 2 units to the left.

This means that

g(x) = f(x + 2)

Then we must have that h = -2.

The correct option is D

y = i/2 xtnop + (3i/2 tnop+ 1)

step-by-step explanation:

the picture is the step by step explanation.

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.