1500 [ randRange( -9, -1 ), randRange( 1, 9 ) ] (function() { var functionPath = []; var prev; var push = function( val ) { prev = val; functionPath.push( prev ); }; push([ DOMAIN[0], randRange( -5, 5 ) ]); for( var i = DOMAIN[0]+1; i <= DOMAIN[1]; i++ ) { if ( abs( randRangeNonZero( -10, 10 ) < 2 ) && prev[1] < 8 ) { push([i, prev[1]+1]); } else if ( abs( randRangeNonZero( -10, 10 ) < 2 ) && prev[1] > -8 ) { push([i, prev[1]-1]); } else if ( abs( randRangeNonZero( -10, 10 ) < 2 ) && prev[1] < 7 ) { push([i, prev[1]+2]); } else if ( abs( randRangeNonZero( -10, 10 ) < 3 ) && prev[1] > -7 ) { push([i, prev[1]-2]); } else { push([i, prev[1]]); } } return functionPath; })() (function() { var values = $.map( FUNCTION_PATH, function( p ) { return p[1]; } ); return [ min.apply( null, values ), max.apply( null, values ) ]; })()

The function `f(x)` is graphed; what is its domain?

graphInit({ range: 10, scale: 20, axisArrows: "<->", tickStep: 1, labelStep: 1, unityLabels: false, labelFormat: function( s ) { return "\\small{" + s + "}"; } }); graph.fn_path = path( FUNCTION_PATH, { stroke: BLUE } ); circle( FUNCTION_PATH[0], 0.15, { stroke: "none", fill: BLUE } ); circle( FUNCTION_PATH[ FUNCTION_PATH.length - 1], 0.15, { stroke: "none", fill: BLUE } );

DOMAIN[0]`\;\le x\le\;`DOMAIN[1]

For what values of `x` does `f(x)` have a value?

Look at the horizontal axis as if it were a number line.

var domain_path = graph.fn_path.clone(); var tmp_path = path( $.map( FUNCTION_PATH, function( p ) { return [[ p[0], 0 ]]; }), { stroke: "none" } ); domain_path.animate( { path: tmp_path.attrs.path, "stroke-width": 4, stroke: GREEN }, ANIM_SPEED, "ease-in-out"); circle( [ FUNCTION_PATH[0][0], 0 ], 0.3, { stroke: "none", fill: GREEN, "fill-opacity": 0 } ) .animate( { "fill-opacity": 1.0 }, ANIM_SPEED, "ease-in-out" ); circle( [ FUNCTION_PATH[ FUNCTION_PATH.length - 1 ][0], 0 ], 0.3, { stroke: "none", fill: GREEN, "fill-opacity": 0 } ) .animate( { "fill-opacity": 1.0 }, ANIM_SPEED, "ease-in-out" ); tmp_path.remove();

`DOMAIN[0]\le x\le DOMAIN[1]`

The function `f(x)` is graphed; what is its range?

RANGE[0]`\;\le f(x)\le\;`RANGE[1]

What values can `f(x)` have?

Look at the vertical axis as if it were a number line.

var range_path = graph.fn_path.clone(); var tmp_path = path( $.map( FUNCTION_PATH, function( p ) { return [[ 0, p[1] ]]; }), { stroke: "none" } ); range_path.animate( { path: tmp_path.attrs.path, "stroke-width": 4, stroke: GREEN }, ANIM_SPEED, "ease-in-out"); circle( [ 0, RANGE[0] ], 0.3, { stroke: "none", fill: GREEN, "fill-opacity": 0 } ) .animate( { "fill-opacity": 1.0 }, ANIM_SPEED, "ease-in-out" ); circle( [ 0, RANGE[1] ], 0.3, { stroke: "none", fill: GREEN, "fill-opacity": 0 } ) .animate( { "fill-opacity": 1.0 }, ANIM_SPEED, "ease-in-out" ); tmp_path.remove();

`RANGE[0]\le f(x)\le RANGE[1]`