Rotation 270 counterclockwise about origin is easy, swap the x and y then reverse the sign of the y so (x, y) rotates to (y, -x) Sadly to change the centre we need to translate the centre to the origin, rotate and the translate back. In this case that means adding -1, 2 to x,y respectively, rotating, adding 1, -2 to x,y respectively
B(2, 3) translates to (1, 5) which rotates to (5, -1) and translates back to B’(6, -3) C(6, -4) translates to (5, -2) which rotates to (-2, -5) and translates back to C’(-1, -7) D(7, -6) translates to (6, -4) which rotates to (-4, -6) and translates back to (-3, -8) E(3, -5) translates to (2, -3) which rotates to (-3, -2) and translates back to (-2, -4)
The translation is much easier simply moving each point 8 to the right B’(2, 11), C’(6, 4), D’(7, 2) and E’(3, 3)
In any case, the domain is restricted to values of the variable for which the function is defined. The value 1/0 is not defined, so the variable cannot allow the denominator to be zero. The denominator x-3 will be zero for x=3, so that value of the variable cannot be in the domain.
The domain is all real numbers except x=3.
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<em>Additional comments</em>
It is useful to become familiar with the domains of different functions. As we saw above, the reciprocal of 0 is undefined. The square root of a negative number is undefined. The log of a non-positive number is undefined. Trig functions are defined everywhere, but their inverse functions are not. Polynomial functions are defined everywhere, but ratios of polynomials have the same restriction on denominators that we see above.
