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For \[f(x) = \frac{2x}{x – 3},\] what is the vertical asympt…

For \[f(x) = \frac{2x}{x – 3},\] what is the vertical asymptote? The x-axis spans from below zero to above 5, and the y-axis spans from below negative 10 to above 10. 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 convex curve is in the first quadrant, passing through the points (3.5, 14) and (6,4). It starts from positive infinity above the vertical asymptote near x= 3. It decreases steeply before leveling off as it approaches the horizontal asymptote near y= 1. The concave curve spans the fourth, and second quadrants, passing through (2, negative 4) and the point slightly below (negative 2, 1). It starts from negative infinity below the vertical asymptote near x= 3, increasing steeply, and then approaching the horizontal asymptote near y =1 in the second quadrant after passing through the origin (0,0). 

The function is \( y = \frac{6}{x^2 – x} \). Which is a vert…

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.