How does one know if the graph is reflected in the x axis due to a negative ''a'' value or there is just a phase shift (Horizontal translation)? Or are they the same thing?
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They are the same thing
for example
y = - sinx is reflected the x-axis
y = - sinx = sin(x + pi) is horizontal translation
for example
y = - sinx is reflected the x-axis
y = - sinx = sin(x + pi) is horizontal translation