(function() { var functionPath = new Array(); functionPath.push([ -11, randRange( -5, 5 ) ]); for( var i = -10; i < 11; i++ ) { if ( abs( randRangeNonZero( -10, 10 ) < 2 ) && functionPath[i+10][1] < 8 ) { functionPath.push([i, functionPath[i+10][1]+1]); } else if ( abs( randRangeNonZero( -10, 10 ) < 2 ) && functionPath[i+10][1] > -8 ) { functionPath.push([i, functionPath[i+10][1]-1]); } else if ( abs( randRangeNonZero( -10, 10 ) < 2 ) && functionPath[i+10][1] < 7 ) { functionPath.push([i, functionPath[i+10][1]+2]); } else if ( 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; })() randRange(-9, 9) FUNCTION_PATH[CORRECT_X + 11][1]

The function `f(x)` is graphed. Find `f(CORRECT_X)`.

graphInit({ range: 10, scale: 20, axisArrows: "<->", tickStep: 1, labelStep: 1, unityLabels: false, labelFormat: function( s ) { return "\\small{" + s + "}"; } }); path( FUNCTION_PATH, { stroke: "#6495ed" } );

CORRECT_Y

At what point does `f(x)` intersect `x = CORRECT_X`?

graph.vert = line( [CORRECT_X, -10], [CORRECT_X, 10], { stroke: "#28ae7b", strokeDasharray: "- " } ); circle( [CORRECT_X, CORRECT_Y], 3/20, { stroke: "none", fill: "black" } );

They intersect at `(CORRECT_X, CORRECT_Y)`.

Thus, `f(CORRECT_X) = CORRECT_Y`.

graph.vert.remove();