1. The problem is to solve the equation and sketch the graph of the function. 2. We start by stating the function to analyze: $$y = \frac{2x^2 - 8}{x - 2}$$. 3. To simplify, factor the numerator: $$2x^2 - 8 = 2(x^2 - 4) = 2(x - 2)(x + 2)$$. 4. Substitute back: $$y = \frac{2(x - 2)(x + 2)}{x - 2}$$. 5. Cancel the common factor $x - 2$ carefully, noting $x \neq 2$ to avoid division by zero: $$y = \frac{2\cancel{(x - 2)}(x + 2)}{\cancel{(x - 2)}} = 2(x + 2)$$. 6. So the simplified function is $$y = 2x + 4$$ for $x \neq 2$. 7. The graph is a straight line with slope 2 and y-intercept 4, but with a hole at $x = 2$. 8. To sketch: - Plot the line $y = 2x + 4$. - Mark a hole (open circle) at the point where $x = 2$, which is $y = 2(2) + 4 = 8$. Final answer: The function simplifies to $$y = 2x + 4$$ with a hole at $x = 2$.