## FANDOM

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Transformations of functions include reflections, stretches, compressions, and shifts.

## Types of transformation

### Reflections

A function $y=f(x)$ can be reflected across the x-axis by multiplying $y$ by -1 to give $-y=f(x)$ or $y=-f(x)$ .

A function can also be reflected across the y-axis by multiplying $x$ by -1, giving $y=f(-x)$ .

A function can be reflected across the line $y=x$ by swapping $x$ and $y$ in the equation, yielding $x=f(y)$ (if $y$ can be isolated, this is equivalent to $y=f^{-1}(x)$ .

### Stretches and compressions

Multiplying $y$ by any constant $a$ will stretch the graph vertically by a factor of the reciprocal of $a$ . Likewise, multiplying $x$ by any constant will do the same horizontally.

### Shifts

Subtracting any constant $k$ from $y$ (or adding it to $f(x)$) will shift the graph up by $k$ units. Subtracting a constant from $x$ (giving $y=f(x-h)$ will shift the graph $h$ units to the right.

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