\color{red}{f(x)}
is graphed in red.
\color{blue}{g(x)}
is graphed in blue.
What is \color{blue}{g(x)}
in terms of \color{red}{f(x)}
?
expr(["+",["*", FLIP, ["*", "f", ["+","x", X_SHIFT]]],Y_SHIFT])
expr(["+",["*", FLIP, ["*", "f", ["+","x", X_SHIFT]]],-Y_SHIFT])
expr(["+",["*", FLIP, ["*", "f", ["+","x", -X_SHIFT]]],Y_SHIFT])
expr(["+",["*", -FLIP, ["*", "f", ["+","x", X_SHIFT]]],Y_SHIFT])
expr(["+",["*", FLIP, ["*", "f", ["+","x", -X_SHIFT]]],-Y_SHIFT])
To get from f(x)
to g(x)
, first "flip" f(x)
vertically by multiplying by -1
, giving -f(x)
.
Shift the function -f(x)
(Y_SHIFT > 0 ? "up " : "down ") + abs(Y_SHIFT) (abs(Y_SHIFT) == 1 ? "unit" : "units"), giving expr(["+",["*", FLIP,"f(x)"], Y_SHIFT])
.
Now shift the function expr(["+",["*", FLIP,"f(x)"], Y_SHIFT])
(X_SHIFT > 0 ? "left " : "right ") + abs(X_SHIFT) (abs(X_SHIFT) == 1 ? "unit" : "units"), giving expr(["+",["*", FLIP, ["*", "f", ["+","x", X_SHIFT]]], Y_SHIFT])
.
We now know that g(x)
= expr(["+",["*", FLIP, ["*", "f", ["+","x", X_SHIFT]]],Y_SHIFT])
.