(function() {
var currentY = randRange( -5, 5 );
var functionPath = new Array();
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 = new Array();
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 f(CORRECT_X) + G_COEF 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