(function() { var currentY = randRange( -5, 5 ); var functionPath = []; functionPath.push([-11, currentY]); for( var i = -10; i < 11; i++ ) { if (Math.abs( randRangeNonZero( -10, 10 ) < 2 ) && functionPath[i+10][1] < 8 ) { functionPath.push([ i, functionPath[i+10][1]+1 ]); } else if (Math.abs( randRangeNonZero( -10, 10 ) < 2 ) && functionPath[i+10][1] > -8 ) { functionPath.push([ i, functionPath[i+10][1]-1 ]); } else if (Math.abs( randRangeNonZero( -10, 10 ) < 2 ) && functionPath[i+10][1] < 7 ) { functionPath.push([ i, functionPath[i+10][1]+2 ]); } else if (Math.abs( randRangeNonZero( -10, 10 ) < 3 ) && functionPath[i+10][1] > -7 ) { functionPath.push([ i, functionPath[i+10][1]-2 ]); } else { functionPath.push([ i, functionPath[i+10][1] ]); } } return functionPath; })() (function() { var gY = randRange( 3, -7 ); var gPath = []; gPath.push([-11, gY]); for( var i = -10; i < 11; i++ ) { if (Math.abs( randRangeNonZero( -10, 10 ) < 2 ) && gPath[i+10][1] < 8 ) { gPath.push([i, gPath[i+10][1]+1]); } else if (Math.abs( randRangeNonZero( -10, 10 ) < 3 ) && gPath[i+10][1] > -8 ) { gPath.push([i, gPath[i+10][1]-1]); } else if (Math.abs( randRangeNonZero( -10, 10 ) < 2 ) && gPath[i+10][1] < 7 ) { gPath.push([i, gPath[i+10][1]+2]); } else if (Math.abs( randRangeNonZero( -10, 10 ) < 3 ) && gPath[i+10][1] > -7 ) { gPath.push([i, gPath[i+10][1]-2]); } else { gPath.push([i, gPath[i+10][1]]); } } return gPath; })() randRangeExclude( -10, 10, [-1, 0, 1] ) randRangeExclude( -10, 10, [-1, 0, 1] ) randRange(-9, 9) FUNCTION_PATH[CORRECT_X + 11][1] randRange(-9, 9) G_PATH[CORRECT_GX+11][1]

Functions f(x) and g(x) are graphed. Find F_COEF \cdot f(CORRECT_X)\space + \spaceG_COEF \cdot g(CORRECT_GX).

graphInit({ range: 10, scale: 20, tickStep: 1, labelStep: 1, unityLabels: false, labelFormat: function( s ) { return "\\small{" + s + "}"; }, axisArrows: "<->" }); path( FUNCTION_PATH, { stroke: "#ffa500" } ); path( G_PATH, { stroke: "#28ae7b" } );

F_COEF * CORRECT_Y + G_COEF * CORRECT_GY

Find f(CORRECT_X) and g(CORRECT_GX).

\begin{align*} f(CORRECT_X) &= CORRECT_Y \\ g(CORRECT_GX) &= CORRECT_GY \end{align*}

F_COEF f(CORRECT_X) + G_COEF g(CORRECT_GX)

= (F_COEF) (CORRECT_Y) + (G_COEF) (CORRECT_GY)

= F_COEF * CORRECT_Y + G_COEF * CORRECT_GY

= F_COEF * CORRECT_Y + G_COEF * CORRECT_GY