randRange(-6, 6) randRange(-6, 6)
generateFunctionPath(END_F) generateFunctionPath(END_G) randRangeExclude(-10, 10, [0, 1]) randRangeExclude(-10, 10, [0, 1]) randRange(-9, 9) F_PATH[CORRECT_X + 10][1] randRange(-9, 9) G_PATH[CORRECT_GX + 10][1]

Functions `\blue{f}` and `\red{g}` are graphed.

`F_COEF \cdot f(CORRECT_X) + G_COEF \cdot g(CORRECT_GX) = {?}`

graphInit({ range: 10, scale: 20, tickStep: 1, labelStep: 1, unityLabels: false, labelFormat: function( s ) { return "\\small{" + s + "}"; }, axisArrows: "<->" }); label([0, 10], "y", "above"); label([10, 0], "x", "right"); label([10, END_F], "y = f(x)", "right", {color: BLUE}); label([10, END_G], "y = g(x)", "right", {color: RED}); path(F_PATH, {stroke: BLUE}); path(G_PATH, {stroke: RED, "stroke-dasharray": "-"});

F_COEF * CORRECT_Y + G_COEF * CORRECT_GY

Find `\blue{f(CORRECT_X)}` and `\red{g(CORRECT_GX)}`.

line([CORRECT_X, 0], [CORRECT_X, CORRECT_Y], { stroke: BLACK, "stroke-dasharray": "." }); circle([CORRECT_X, CORRECT_Y], 0.2, { stroke: null, fill: BLUE });

`\blue{f(CORRECT_X) = CORRECT_Y}`

line([CORRECT_GX, 0], [CORRECT_GX, CORRECT_GY], { stroke: BLACK, "stroke-dasharray": "." }); circle([CORRECT_GX, CORRECT_GY], 0.2, { stroke: null, fill: RED });

`\red{g(CORRECT_GX) = CORRECT_GY}`

`F_COEF \cdot \blue{f(CORRECT_X)} + G_COEF \cdot \red{g(CORRECT_GX)} = coefficient(F_COEF)(\blue{CORRECT_Y}) + coefficient(G_COEF)(\red{CORRECT_GY})`

`= F_COEF * CORRECT_Y + G_COEF * CORRECT_GY`

`= F_COEF * CORRECT_Y + G_COEF * CORRECT_GY`