Question

graph the rational function.
( g(x) = \frac{x^2 - 8x + 16}{x - 4} )
start by drawing the asymptotes (if there are any). then plot two points on each piece of the graph. finally, click on the graph - a - function button. be sure to plot a hollow dot wherever there is a \hole\ in the graph.

Explanation:

Step1: Factor numerator

The numerator is a quadratic; factor it.
$x^2 -8x +16=(x-4)^2$

Step2: Simplify the function

Cancel common factors (where $x
eq4$).
$g(x)=\frac{(x-4)^2}{x-4}=x-4, \quad x
eq4$

Step3: Identify the hole

Find the hole's coordinates.
At $x=4$, $g(4)=4-4=0$, so hole at $(4,0)$.

Step4: Plot points for the line

Choose $x=0$: $g(0)=0-4=-4$, so point $(0,-4)$.
Choose $x=6$: $g(6)=6-4=2$, so point $(6,2)$.
Choose $x=2$: $g(2)=2-4=-2$, so point $(2,-2)$.
Choose $x=-2$: $g(-2)=-2-4=-6$, so point $(-2,-6)$.

Answer:

1. Draw the line $y=x-4$ (a straight line with slope 1, y-intercept -4).
2. Plot a hollow dot at the point $(4, 0)$ (the hole in the graph, since $x=4$ makes the original function undefined).
3. Plot the points $(0,-4)$, $(6,2)$, $(2,-2)$, $(-2,-6)$ (or any two points on each "side" of the hole) on the line.