f(x - X_SHIFT)f(x) + X_SHIFTf(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)}.
This means the value of \red{g} at a number x is the same as the value
of \blue{f} at a number 1 more than x.
This means the value of \red{g} at a number x is the same as the value
of \blue{f} at a number abs(X_SHIFT) more than x.
This means the value of \red{g} at a number x is the same as the value
of \blue{f} at a number 1 less than x.
This means the value of \red{g} at a number x is the same as the value
of \blue{f} at a number abs(X_SHIFT) less than x.
What would this sentence look like as an equation?
g(x) = ANSWER
f(x + Y_SHIFT)f(x - Y_SHIFT)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)}.
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.
f(toFractionTex(1/X_COEFFICIENT)x)f(toFractionTex(X_COEFFICIENT)x)toFractionTex(1/X_COEFFICIENT)f(x)toFractionTex(-1/X_COEFFICIENT)f(x)toFractionTex(-X_COEFFICIENT)f(x)
Function \red{g(x)} is flipped vertically compared to \blue{f(x)},
so we should multiply by -1 reflect it over the x-axis.
This new function, \green{-f(x)} is closer to \red{g(x)}, but they are still not equal.
What else do we need to do?
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
\green{-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 relative to
\green{-f(x)}
\blue{f(x)},
so must be multiplied by a number with a magnitude greater than 1.
g(x) = ANSWER.f(toFractionTex(1/Y_COEFFICIENT)x)f(toFractionTex(-1/Y_COEFFICIENT)x)f(toFractionTex(-Y_COEFFICIENT)x)toFractionTex(1/Y_COEFFICIENT)f(x)toFractionTex(Y_COEFFICIENT)f(x)
Function \red{g(x)} is flipped horizontally compared to \blue{f(x)},
so we should multiply x by -1 reflect it over the y-axis.
This new function, \green{f(-x)} is closer to \red{g(x)}, but they are still not equal.
What else do we need to do?
Function \red{g(x)} is stretched horizontally relative to
\green{f(-x)}
\blue{f(x)},
so must be multiplied by a number with a magnitude less than 1.
Function \red{g(x)} is compressed horizontally relative to
\green{f(-x)}
\blue{f(x)},
so must be multiplied by a number with a magnitude greater than 1.
g(x) = ANSWER.
\red{g(x)} is a transformation of \blue{f(x)}.
The graph below shows \blue{f(x)} as a solid blue line and
\red{g(x)} as a dotted red line.
What is \red{g(x)} in terms of \blue{f(x)}?
ANSWER