# How do you find the domain, points of discontinuity and the x and y intercepts of the rational function #y=(12-6x)/(x^2-8x+12)#?

Domain :

Points of discontinuity are

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To find the domain of the rational function ( y = \frac{12 - 6x}{x^2 - 8x + 12} ), you need to determine the values of ( x ) for which the function is defined. The function is defined for all ( x ) except those that make the denominator equal to zero. Thus, the domain is all real numbers except the values that make ( x^2 - 8x + 12 = 0 ).

To find the points of discontinuity, you need to identify the values of ( x ) where the function has vertical asymptotes or holes. These occur where the denominator is equal to zero but the numerator is not. To find these points, solve the equation ( x^2 - 8x + 12 = 0 ) and determine if the solutions make the numerator non-zero.

To find the ( x )-intercepts, set ( y = 0 ) and solve for ( x ). These are the points where the function crosses the ( x )-axis.

To find the ( y )-intercept, set ( x = 0 ) and solve for ( y ). This is the point where the function crosses the ( y )-axis.

Once you have determined these values, you'll have the domain, points of discontinuity, and the ( x )- and ( y )-intercepts of the rational function.

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