Eraphing a rational function: Const Graph the rational function. \[ f(x)=\frac{8}{-x+2} \] Start by drawing the vertical and \( h \)

To graph the rational function \( f(x) = \frac{8}{-x + 2} \), begin by identifying the vertical asymptote. Set the denominator equal to zero to find where the function is undefined: \(-x + 2 = 0\) leads to \(x = 2\). This means there is a vertical asymptote at \(x = 2\). For the horizontal asymptote, since the degree of the numerator (0) is less than the degree of the denominator (1), the horizontal asymptote is at \(y = 0\). Next, calculate a few values to sketch the graph. For \(x < 2\), such as \(x = 0\), \(f(0) = \frac{8}{2} = 4\). For \(x > 2\), like \(x = 4\), \(f(4) = \frac{8}{-2} = -4\). Plot these points, keeping in mind the behavior approaching the asymptotes: the graph approaches the vertical asymptote at \(x = 2\) as it increases towards infinity from the left and decreases towards negative infinity from the right. To avoid confusion while graphing, remember that rational functions can have holes. A common mistake is forgetting to check for factors that cancel. In this case, since there are no common factors, your curve will properly exhibit behavior as described without any holes. Enjoy graphing!