randRange(-4, 4) randRange(-3, 3) randRangeNonZero(-1, 1) randFromArray([ function(x) { return 0.25 * UP_ORIG * pow(x + X_ORIG, 2) + Y_ORIG; }, function(x) { return 0.02 * UP_ORIG * (pow(x + X_ORIG, 3) + 10 * pow(x + X_ORIG, 2)) + Y_ORIG; } ])
X_ORIG > 0 ? randRange(-6, -1) : randRange(1, 6) 1 0 expr(["*", "f", ["+", "x", X_SHIFT]])
  • expr(["*", "f", ["+","x", -X_SHIFT]])
  • expr(["+", "f(x)", X_SHIFT])
  • expr(["+", "f(x)", -X_SHIFT])

Function \red{g(x)} is shifted 1 unit left relative to \blue{f(x)}. Function \red{g(x)} is shifted abs(X_SHIFT) units left relative to \blue{f(x)}.

Function \red{g(x)} is shifted 1 unit right relative to \blue{f(x)}. Function \red{g(x)} is shifted abs(X_SHIFT) units right relative to \blue{f(x)}.

style({ stroke: BLACK, strokeWidth: 2, arrows: "->", }); path([[-X_ORIG, COEFFICIENT * Y_ORIG + Y_SHIFT], [-X_ORIG - X_SHIFT , COEFFICIENT * Y_ORIG + Y_SHIFT]]);

Therefore, to find \red{g(x)} you can find the value of \blue{f(x)} 1 unit to the right. Therefore, to find \red{g(x)} you can find the value of \blue{f(x)} abs(X_SHIFT) units to the right.

Therefore, to find \red{g(x)} you can find the value of \blue{f(x)} 1 unit to the left. Therefore, to find \red{g(x)} you can find the value of \blue{f(x)} abs(X_SHIFT) units to the left.

Therefore g(x) = ANSWER.

0 1 randRangeNonZero(-6, 6) expr(["+", "f(x)", Y_SHIFT])
  • expr(["*", "f", ["+","x", Y_SHIFT]])
  • expr(["*", "f", ["+","x", -Y_SHIFT]])
  • expr(["+", "f(x)", -Y_SHIFT])

Function \red{g(x)} is shifted 1 unit up relative to \blue{f(x)}. Function \red{g(x)} is shifted abs(Y_SHIFT) units up relative to \blue{f(x)}.

Function \red{g(x)} is shifted 1 unit down relative to \blue{f(x)}. Function \red{g(x)} is shifted abs(Y_SHIFT) units down relative to \blue{f(x)}.

style({ stroke: BLACK, strokeWidth: 2, arrows: "->", }); path([[-X_ORIG, COEFFICIENT * Y_ORIG], [-X_ORIG, COEFFICIENT * Y_ORIG + Y_SHIFT]]);

Therefore, to find \red{g(x)} you can find \blue{f(x)} and add abs(Y_SHIFT).

Therefore, to find \red{g(x)} you can find \blue{f(x)} and subtract abs(Y_SHIFT).

Therefore g(x) = ANSWER.

0 randFromArray([-1, 1]) * randFromArray([1/3, 0.5, 2, 3]) 0 toFractionTex(COEFFICIENT) + "f(x)"
  • toFractionTex(1/COEFFICIENT)f(x)
  • toFractionTex(-1/COEFFICIENT)f(x)
  • toFractionTex(-COEFFICIENT)f(x)

Function \red{g(x)} is flipped vertically compared to \blue{f(x)}, so multiply by -1 to get \color{red}{-f(x)}.

style({ stroke: GREEN, strokeDasharray: "- " }); plot( function(x) { return -FUNC(x); }, [-10, 10]);

Function \red{g(x)} is not flipped vertically compared to \blue{f(x)}, so does not have a negative coefficient.

Function \red{g(x)} is compressed vertically relative to \color{red}{-f(x)} \blue{f(x)}, so must be multiplied by a number with a magnitude less than 1.

Function \red{g(x)} is stretched vertically compared to \color{red}{-f(x)} \blue{f(x)}, so must be multiplied by a number with a magnitude greater than 1.

Therefore g(x) = ANSWER.

Functions \blue{f(x)} and \red{g(x)} are graphed.

What is \red{g(x)} in terms of \blue{f(x)}?

graphInit({ range: 10, scale: 20, labelStep: 1, axisArrows: "<->" }) style({ stroke: BLUE, strokeWidth: 2, arrows: null }); plot(function(x) { return FUNC(x); }, [-10, 10]); style({ stroke: RED }); plot(function(x) { return COEFFICIENT * FUNC(x + X_SHIFT) + Y_SHIFT; }, [-10, 10]);

ANSWER