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)?

May 19, 2017

Domain : $x \in \mathbb{R} , x \ne 6$ or $\left(- \infty , 6\right) \cup \left(6 , \infty\right)$
Points of discontinuity are $x = 6 , x = 2$, x intercept as $x = 2$, y intercept as $y = 1$

Explanation:

$y = \frac{12 - 6 x}{{x}^{2} - 8 x + 12} \mathmr{and} y = \frac{- 6 \cancel{\left(x - 2\right)}}{\left(x - 6\right) \cancel{\left(x - 2\right)}}$ or

$y = - \frac{6}{x - 6}$ domain : x !=6 ,$x \in \mathbb{R} , x \ne 6$ or $\left(- \infty , 6\right) \cup \left(6 , \infty\right)$

Points of discontinuity are $x = 6 , x = 2$, but $x = 2$ is removable discontinuity.
Putting $x = 0$ we get y intercept as $y = \frac{12}{12} = 1$

Putting $y = 0$ we get x intercept as $12 - 6 x = 0 \mathmr{and} x = 2$