Which of the following represents the factorization of \( x^3 – 3x^2 – 4x + 12 \)?

The function is \( y = \frac{6}{x^2 – x} \). Which is a vertical asymptote of this function? The x-axis spans from below negative 5 to beyond 5, and the y-axis spans from below negative 40 to above 20. The x-axis has a scale of 5 in increments of 1, and the y-axis has a scale of 20 in increments of 5. The red rational function consists of two convex curves in the first and second quadrants, with a narrow, bounded region with single peak below the x-axis. The first-quadrant convex curve starts from positive infinity near the vertical line x = 1, decreases sharply, and then approaches the horizontal asymptote along the positive x-axis. The second quadrant convex curve starts from positive infinity near x = 0, decreases toward the negative x-axis, and extends horizontally. A single narrow peak appears in the fourth quadrant near the point (0.5, negative 24), where the function briefly rises before decreasing again. This localized fluctuation is confined to a narrow, bounded region in between x = 0 and x = 1. 

For the function \( f(x) = \frac{x + 3}{x – 2} \), what is the horizontal asymptote?

For the function \( f(x) = \frac{x}{x – 3} \), the vertical asymptote is at:

For the function \( f(x) = \frac{2}{x – 1} \), the vertical asymptote is at:

Which of the following represents a rational function with a vertical asymptote at \( x = 4 \)?

What type of discontinuity occurs at \( x = -1 \) for \( f(x) = \frac{x^2 – 1}{x + 1} \)?

How can you find the x-intercept of \[f(x) = \frac{3x + 6}{x – 4}?\]

Which is one of the transformations to  represented in the graph? The x-axis spans from negative 5 to 10, and the y-axis spans from below 0 to just above 20. The x-axis has a scale of 5 in increments of 1, and the y-axis has a scale of 10 in increments of 2. The blue parabolic function opens upward and has a minimum vertex at (3, 1). The parabola is symmetric around the vertical line passing through the vertex and passes through the coordinates (0, 20) and (6, 20).

For the function \[f(x) = \frac{x – 3}{x^2 – x – 6},\] what are the vertical asymptotes?