1. q(x) = (4x² - 4x + 1) / (2x² - 5x + 2)
- This graph shows a rational function with vertical asymptotes and a horizontal asymptote.
2. S(x) = (16x² - 9) / (4x - 3)³
- The graph has a vertical asymptote at ( x = \frac{3}{4} \) and exhibits rapid changes near the asymptote.
3. T(x) = (x² - 5x - 24) / (x + 3)
- This graph has a vertical asymptote at \( x = -3 \) and shows a slant asymptote as the degree of the numerator is one more than the denominator.
4. U(x) = (x - 6)³ / (x² - 36)
- The graph has vertical asymptotes at ( x = 6 \) and \( x = -6 ), reflecting significant changes near these points.
5. V(x) = (x³ - 1) / (x² - 2x + 1)
- The graph has a vertical asymptote at ( x = 1 \) and shows distinct behavior near this asymptote.
