If you take a graph and transform it in various ways, here is what you get:
A reflection in the y-axis turns a graph of y=f(x) into the graph of y= f(-x).
A reflection in the x-axis turns a graph of y=f(x) into the graph of y= -f(x)
- note the difference -
A stretch of factor s in the y- direction turns the graph of y= f(x) into the graph of
y = s f(x).
A stretch of factor m in the x-direction turns the graph of y = f(x) into the graph of \[y = f(\frac{x}{m})\]
A translation by \[ \left( \frac{k}{l} \right) \] turns the graph of y = f(x) into the graph of y = f(x-k) + l
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