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

Functions f(x) and g(x) are graphed.

Find 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([10, END_F], "f(x)", "right", {color: BLUE}); label([10, END_G], "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 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