Function Graphs Bronze

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y=-{x}^{3}+19{x}^{2}-114x+216\phantom{\rule{0ex}{0ex}}y={x}^{2}-10x+24\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(6,0\right)\text{, }\left(8,8\right)\text{ and }\left(4,0\right)\)

y = 1⁄-3f(x)
y = -5f(x)
y = -2f(x)
y = -3f(x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y=-{x}^{3}-10{x}^{2}-33x-36\phantom{\rule{0ex}{0ex}}y={x}^{2}+5x+4\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(-2,-2\right)\text{, }\left(-4,0\right)\text{ and }\left(-5,4\right)\)

y = -2f(x)
y = -1f(x)
y = 1⁄-4f(x)
y = 0f(x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y=-{x}^{3}-19{x}^{2}-114x-216\phantom{\rule{0ex}{0ex}}y={x}^{2}+13x+36\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(-4,0\right)\text{, }\left(-7,-6\right)\text{ and }\left(-9,0\right)\)

y = 1⁄-3f(x)
y = 1⁄-4f(x)
y = -2f(x)
y = 1⁄-2f(x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y={x}^{3}+7{x}^{2}+7x-15\phantom{\rule{0ex}{0ex}}y={x}^{2}+4x-5\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(-2,-9\right)\text{, }\left(1,0\right)\text{ and }\left(-5,0\right)\)

y = f(1⁄-3x)
y = f(-3x)
y = f(1⁄-5x)
y = f(1⁄-4x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y=-{x}^{3}+4{x}^{2}-x-6\phantom{\rule{0ex}{0ex}}y=2{x}^{2}-4x-6\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(3,0\right)\text{, }\left(0,-6\right)\text{ and }\left(-1,0\right)\)

y = -2f(x)
y = -1f(x)
y = 1⁄-2f(x)
y = -3f(x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y={x}^{3}-2{x}^{2}-5x+6\phantom{\rule{0ex}{0ex}}y=2{x}^{2}-8x+6\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(3,0\right)\text{, }\left(1,0\right)\text{ and }\left(0,6\right)\)

y = 1⁄-2f(x)
y = -1f(x)
y = 1⁄-1f(x)
y = -2f(x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y=-{x}^{3}+2{x}^{2}+5x-6\phantom{\rule{0ex}{0ex}}y={x}^{2}-x-6\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(3,0\right)\text{, }\left(0,-6\right)\text{ and }\left(-2,0\right)\)

y = f(1⁄-2x)
y = f(-2x)
y = f(-4x)
y = f(1⁄-4x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y=-{x}^{3}-{x}^{2}+9x+9\phantom{\rule{0ex}{0ex}}y={x}^{2}-9\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(3,0\right)\text{, }\left(-2,-5\right)\text{ and }\left(-3,0\right)\)

y = 1⁄-3f(x)
y = 1⁄-5f(x)
y = 1⁄-4f(x)
y = -1f(x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y=-{x}^{3}+4{x}^{2}-x-6\phantom{\rule{0ex}{0ex}}y=2{x}^{2}-4x-6\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(3,0\right)\text{, }\left(0,-6\right)\text{ and }\left(-1,0\right)\)

y = -2f(x)
y = -4f(x)
y = 1⁄-1f(x)
y = 1⁄-2f(x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y=-{x}^{3}+15{x}^{2}-71x+105\phantom{\rule{0ex}{0ex}}y={x}^{2}-10x+21\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(7,0\right)\text{, }\left(4,-3\right)\text{ and }\left(3,0\right)\)

y = f(1⁄-3x)
y = f(-3x)
y = f(1⁄-4x)
y = f(1⁄-5x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y={x}^{3}+4{x}^{2}-x-4\phantom{\rule{0ex}{0ex}}y={x}^{2}-1\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(-1,0\right)\text{, }\left(1,0\right)\text{ and }\left(-3,8\right)\)

y = 1⁄-2f(x)
y = -3f(x)
y = -2f(x)
y = 1⁄-3f(x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y={x}^{3}+7{x}^{2}+7x-15\phantom{\rule{0ex}{0ex}}y={x}^{2}+2x-3\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(1,0\right)\text{, }\left(-3,0\right)\text{ and }\left(-4,5\right)\)

y = f(-3f(x)
y = f(-5x)
y = f(1⁄-4x)
y = f(-4x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y=-{x}^{3}-12{x}^{2}-39x-28\phantom{\rule{0ex}{0ex}}y=2{x}^{2}+22x+56\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(-3,8\right)\text{, }\left(-4,0\right)\text{ and }\left(-7,0\right)\)

y = f(1⁄-3x)
y = f(1⁄-1x)
y = f(1⁄-4x)
y = f(-5x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y=-{x}^{3}-6{x}^{2}-11x-6\phantom{\rule{0ex}{0ex}}y={x}^{2}+x-6\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(0,-6\right)\text{, }\left(-3,0\right)\text{ and }\left(-4,6\right)\)

y = -2f(x)
y = -4f(x)
y = 1⁄-4f(x)
y = -1f(x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y=-{x}^{3}+7{x}^{2}-7x-15\phantom{\rule{0ex}{0ex}}y={x}^{2}-2x-3\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(4,5\right)\text{, }\left(3,0\right)\text{ and }\left(-1,0\right)\)

y = f(-3f(x)
y = f(1⁄-2x)
y = f(1⁄-1x)
y = f(-1x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y=-{x}^{3}-11{x}^{2}-31x-21\phantom{\rule{0ex}{0ex}}y={x}^{2}+8x+7\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(-4,-9\right)\text{, }\left(-1,0\right)\text{ and }\left(-7,0\right)\)

y = 1⁄-2f(x)
y = -2f(x)
y = 1⁄-3f(x)
y = 0f(x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y={x}^{3}+14{x}^{2}+64x+96\phantom{\rule{0ex}{0ex}}y={x}^{2}+10x+24\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(-3,3\right)\text{, }\left(-4,0\right)\text{ and }\left(-6,0\right)\)

y = f(1⁄-2x)
y = f(-4x)
y = f(1⁄-4x)
y = f(0x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y=-{x}^{3}-13{x}^{2}-50x-56\phantom{\rule{0ex}{0ex}}y={x}^{2}+11x+28\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(-3,4\right)\text{, }\left(-4,0\right)\text{ and }\left(-7,0\right)\)

y = f(-3f(x)
y = f(-2x)
y = f(-5x)
y = f(-1x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y=-{x}^{3}-13{x}^{2}-56x-80\phantom{\rule{0ex}{0ex}}y={x}^{2}+7x+10\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(-3,-2\right)\text{, }\left(-5,0\right)\text{ and }\left(-6,4\right)\)

y = 1⁄-3f(x)
y = -5f(x)
y = 1⁄-4f(x)
y = -4f(x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y=-{x}^{3}-18{x}^{2}-107x-210\phantom{\rule{0ex}{0ex}}y={x}^{2}+11x+30\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(-5,0\right)\text{, }\left(-6,0\right)\text{ and }\left(-8,6\right)\)

y = -2f(x)
y = 1⁄-4f(x)
y = 1⁄-1f(x)
y = -1f(x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y={x}^{3}+{x}^{2}-9x-9\phantom{\rule{0ex}{0ex}}y={x}^{2}-2x-3\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(3,0\right)\text{, }\left(-1,0\right)\text{ and }\left(-2,5\right)\)

y = 1⁄-2f(x)
y = 0f(x)
y = 1⁄-4f(x)
y = -3f(x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y=-{x}^{3}-5{x}^{2}+x+5\phantom{\rule{0ex}{0ex}}y={x}^{2}+4x-5\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(-2,-9\right)\text{, }\left(1,0\right)\text{ and }\left(-5,0\right)\)

y = 1⁄-2f(x)
y = 1⁄-1f(x)
y = -1f(x)
y = 0f(x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y=-{x}^{3}+7{x}^{2}-14x+8\phantom{\rule{0ex}{0ex}}y={x}^{2}-6x+8\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(2,0\right)\text{, }\left(4,0\right)\text{ and }\left(0,8\right)\)

y = f(-2f(x)
y = f(1⁄-1x)
y = f(1⁄-4x)
y = f(-1x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y={x}^{3}+4{x}^{2}-4x-16\phantom{\rule{0ex}{0ex}}y={x}^{2}+2x-8\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(-1,-9\right)\text{, }\left(2,0\right)\text{ and }\left(-4,0\right)\)

y = -2f(x)
y = 1⁄-4f(x)
y = -1f(x)
y = -3f(x)

\(\text{Find the area between the lines:}\phantom{\rule{0ex}{0ex}}y=-{x}^{3}+17{x}^{2}-87x+135\phantom{\rule{0ex}{0ex}}y={x}^{2}-12x+27\phantom{\rule{0ex}{0ex}}\text{Intersecting at }\left(9,0\right)\text{, }\left(4,-5\right)\text{ and }\left(3,0\right)\)

y = -3f(x)
y = 1⁄-3f(x)
y = 1⁄-2f(x)
y = 1⁄-5f(x)

\(\text{Three forces act on an object:}\phantom{\rule{0ex}{0ex}}\left[\begin{array}{c}20\\ -30\end{array}\right]N,\left[\begin{array}{c}-15\\ 25\end{array}\right]N\text{ and }\left[\begin{array}{c}13\\ -17\end{array}\right]N\phantom{\rule{0ex}{0ex}}\\\text{Find the magnitude and direction of the resultant force on the object.}\)