y=根號(hào)(x^2+1)+根號(hào)[(2-x)^2+4]=根號(hào){(x-0)^2+[0-(-1)]^2}+根號(hào)[(x-2)^2+(0-2)^2]
表示x軸上的動(dòng)點(diǎn)(x,0)與兩定點(diǎn)(0,-1)和(2,2)的距離和,
兩定點(diǎn)(0,-1)和(2,2)在x軸的兩側(cè),當(dāng)點(diǎn)(x,0)與兩定點(diǎn)(0,-1)和(2,2)共線時(shí),
動(dòng)點(diǎn)(x,0)與兩定點(diǎn)(0,-1)和(2,2)的距離和最小,最小值為兩定點(diǎn)(0,-1)與(2,2)的距離=根號(hào)[(0-2)^2+(-1-2)^2]=根號(hào)13,當(dāng)動(dòng)點(diǎn)(x,0)從與兩定點(diǎn)(0,-1)和(2,2)共線位置開始沿x軸向x軸正方向或負(fù)方向運(yùn)動(dòng)時(shí),動(dòng)點(diǎn)(x,0)與兩定點(diǎn)(0,-1)和(2,2)的距離和不斷增大,即y=根號(hào)(x^2+1)+根號(hào)[(2-x)^2+4]的最小值為根號(hào)13,無(wú)最大值,值域?yàn)閇根號(hào)13,+無(wú)窮).