The graphs:
1. F(x) = 3x^3 - 15x^2 + 18x
Extra points: (1, 6), (2, 12), (4, 24), (6, 54), (7, 81), (8, 108), (9, 135)
2. F(x) = -4x^3 + 4x^2 + 15x
Extra points: (2, 10), (3, 21), (4, 32), (5, 35), (6, 24), (7, -7), (8, -64), (9, -153)
3. F(x) = -5x^2 - x^3
Extra points: (1, -6), (2, -17), (4, -69), (6, -171), (7, -238), (8, -295), (9, -342)
4. F(x) = -48x^2 + 3x^4
Extra points: (1, -45), (2, -24), (3, -9), (4, 0), (5, -9), (6, -24), (7, -45), (8, -72), (9, -105)
To find the LH, RH, x, and y-intercepts, we need to plot the graphs of the given functions. Here are the graphs:
F(x) = 3x^3 - 15x^2 + 18x
Graph of F(x) = 3x^3 - 15x^2 + 18x
LH intercept: None
RH intercept: None
x-intercept: (0, 0), (5, 0), (3, 0)
y-intercept: (0, 0)
Extra points: (1, 6), (2, 12), (4, 24), (6, 54), (7, 81), (8, 108), (9, 135)
F(x) = -4x^3 + 4x^2 + 15x
Graph of F(x) = -4x^3 + 4x^2 + 15x
LH intercept: None
RH intercept: None
x-intercept: (0, 0), (1.5, 0), (-1, 0)
y-intercept: (0, 0)
Extra points: (2, 10), (3, 21), (4, 32), (5, 35), (6, 24), (7, -7), (8, -64), (9, -153)
F(x) = -5x^2 - x^3
Graph of F(x) = -5x^2 - x^3
LH intercept: None
RH intercept: None
x-intercept: (0, 0), (-5, 0), (-3, 0)
y-intercept: (0, 0)
Extra points: (1, -6), (2, -17), (4, -69), (6, -171), (7, -238), (8, -295), (9, -342)
F(x) = -48x^2 + 3x^4
Graph of F(x) = -48x^2 + 3x^4
LH intercept: None
RH intercept: None
x-intercept: (0, 0), (2sqrt(2), 0), (-2sqrt(2), 0)
y-intercept: (0, 0)
Extra points: (1, -45), (2, -24), (3, -9), (4, 0), (5, -9), (6, -24), (7, -45), (8, -72), (9, -105)