Write the equation of the circle that has a diameter with endpoints (3,7)
and (3, 1)

(x - 3)^2 + (y - 4)^2 = 3^2

Step-by-step explanation:

Notice that both endpoints are on the vertical line x = 3.  Thus, to determine the diameter of this circle, we need only subtract 1 from 7, obtaining 6.  The diameter is 6, so the radius is 3.

The center is on the vertical line x = 3 and is halfway between the endpoints of the diameter, that is, at y = 4.  (3, 4) describes this point.

Then we insert the known quantities into the general equation for a circle with center at (h, k) and radius r:  3 for h, 4 for k and 3 for r:

(x - 3)^2 + (y - 4)^2 = 3^2 is the desired equation.

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.