0\; \; ;\; \; (-1,8)^4>0\; \; ;\; \; (0,2)^3>0\; \; \to \; \; (0,2)^3>2\\\\\\3)\; \; a=1:\; \; 2a^3-1=2-1=1\\\\a=-2:\; \; 2a^3-1=2\cdot (-8)-1=-17\\\\a=0:\; \; 2a^3-1=0-1=-1\\\\x=-1:\; \; 16-3x^4=16-3\cdot 1=13\\\\x=2:\; \; 16-3x^4=16-3\cdot 16=-32\\\\x=0:\; \; 16-3x^4=16-0=16" alt="1)\; \; 3^4=3\cdot 3\cdot 3=27\\\\(-5)^3=(-5)\cdot (-5)\cdot (-5)=-125\\\\(\frac{2}{7})^4=\frac{2^4}{7^4}=\frac{16}{2401}\\\\\\2)\; \; 3,2^5>0\; \; ;\; \; (-1,8)^4>0\; \; ;\; \; (0,2)^3>0\; \; \to \; \; (0,2)^3>2\\\\\\3)\; \; a=1:\; \; 2a^3-1=2-1=1\\\\a=-2:\; \; 2a^3-1=2\cdot (-8)-1=-17\\\\a=0:\; \; 2a^3-1=0-1=-1\\\\x=-1:\; \; 16-3x^4=16-3\cdot 1=13\\\\x=2:\; \; 16-3x^4=16-3\cdot 16=-32\\\\x=0:\; \; 16-3x^4=16-0=16" align="absmiddle" class="latex-formula">
![4)\; \; y=\frac{1}{3}\, x-4\\\\OX:\; \; y=0\; ,\; \frac{1}{3}\, x-4=0\; \; \to \; \; \frac{1}{3}\, x=4\; \; ,\; \; x=4\cdot 3=12\; ;\; \; (12;0)\\\\OY:\; \; x=0\; ,\; y=\frac{1}{3}\cdot 0-4\; \; \to \; \; y=-4\; \; ;\; \; (0;-4) 4)\; \; y=\frac{1}{3}\, x-4\\\\OX:\; \; y=0\; ,\; \frac{1}{3}\, x-4=0\; \; \to \; \; \frac{1}{3}\, x=4\; \; ,\; \; x=4\cdot 3=12\; ;\; \; (12;0)\\\\OY:\; \; x=0\; ,\; y=\frac{1}{3}\cdot 0-4\; \; \to \; \; y=-4\; \; ;\; \; (0;-4)](https://tex.z-dn.net/?f=4%29%5C%3B%20%5C%3B%20y%3D%5Cfrac%7B1%7D%7B3%7D%5C%2C%20x-4%5C%5C%5C%5COX%3A%5C%3B%20%5C%3B%20y%3D0%5C%3B%20%2C%5C%3B%20%5Cfrac%7B1%7D%7B3%7D%5C%2C%20x-4%3D0%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20%5Cfrac%7B1%7D%7B3%7D%5C%2C%20x%3D4%5C%3B%20%5C%3B%20%2C%5C%3B%20%5C%3B%20x%3D4%5Ccdot%203%3D12%5C%3B%20%3B%5C%3B%20%5C%3B%20%2812%3B0%29%5C%5C%5C%5COY%3A%5C%3B%20%5C%3B%20x%3D0%5C%3B%20%2C%5C%3B%20y%3D%5Cfrac%7B1%7D%7B3%7D%5Ccdot%200-4%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20y%3D-4%5C%3B%20%5C%3B%20%3B%5C%3B%20%5C%3B%20%280%3B-4%29)
5) a) Прямая проходит через точки (2,1) и (0,2) Подставим координаты этих точек в уравнение прямой y=kx+b:
![\left \{ {{1=k\cdot 2+b} \atop {2=k\cdot 0+b}} \right.\; \; \left \{ {{2k=1-b} \atop {b=2}} \right. \; \; \left \{ {{2k=-1} \atop {b=2}} \right. \; \; \left \{ {{k=-\frac{1}{2}} \atop {b=2}} \right. \\\\y=-\frac{1}{2}\, x+2\\\\b)\; \; (0,0):\; \; y=-\frac{1}{2}\, x+0\; \; \to \; \; y=-\frac{1}{2}\, x \left \{ {{1=k\cdot 2+b} \atop {2=k\cdot 0+b}} \right.\; \; \left \{ {{2k=1-b} \atop {b=2}} \right. \; \; \left \{ {{2k=-1} \atop {b=2}} \right. \; \; \left \{ {{k=-\frac{1}{2}} \atop {b=2}} \right. \\\\y=-\frac{1}{2}\, x+2\\\\b)\; \; (0,0):\; \; y=-\frac{1}{2}\, x+0\; \; \to \; \; y=-\frac{1}{2}\, x](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7B1%3Dk%5Ccdot%202%2Bb%7D%20%5Catop%20%7B2%3Dk%5Ccdot%200%2Bb%7D%7D%20%5Cright.%5C%3B%20%5C%3B%20%5Cleft%20%5C%7B%20%7B%7B2k%3D1-b%7D%20%5Catop%20%7Bb%3D2%7D%7D%20%5Cright.%20%5C%3B%20%5C%3B%20%5Cleft%20%5C%7B%20%7B%7B2k%3D-1%7D%20%5Catop%20%7Bb%3D2%7D%7D%20%5Cright.%20%5C%3B%20%5C%3B%20%5Cleft%20%5C%7B%20%7B%7Bk%3D-%5Cfrac%7B1%7D%7B2%7D%7D%20%5Catop%20%7Bb%3D2%7D%7D%20%5Cright.%20%5C%5C%5C%5Cy%3D-%5Cfrac%7B1%7D%7B2%7D%5C%2C%20x%2B2%5C%5C%5C%5Cb%29%5C%3B%20%5C%3B%20%280%2C0%29%3A%5C%3B%20%5C%3B%20y%3D-%5Cfrac%7B1%7D%7B2%7D%5C%2C%20x%2B0%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20y%3D-%5Cfrac%7B1%7D%7B2%7D%5C%2C%20x)