What is the domain of the rational function, f of x equals quantity x minus 5 over quantity 2 times x minus 3

Domain = R - {3/2}

Step-by-step explanation:

The domain of a rational function consists of all the real numbers x except those for which the denominator is 0

The given function is :

We need to find the zeros of the denominator

∴ 2x - 3 = 0    ⇒ add 3 to both sides

∴ 2x = 3          ⇒ divide both side by 2

∴ x = 3/2        

The domain will be all real number except the zeros of the denominator.

So, Domain = R - {3/2}

Also, see the attached figure that represents the given function.

i can try and you the very best that i can.

step-by-step explanation:

through just a quick inspection, one can see that the graph of this cubing function starts in quadrant iii and ends in quadrant i.   when x = 0, y = 3, so the y-intercept is (0, 3).

if graphs are part of the problem statement, share them.   .