If g(x) is a logarithmic function, then what effect does 'c' have on g(x) if f(x) = g(cx)?
a. g(x) shifts c units to the sign opposite of c
b. g(x) stretches or shrinks horizontally
c. g(x) stretches vertically
d. There is no effect on g(x)
This is a poorly written problem. If 'c' were = 1 then there
is no effect and the answer would be d. If 'c' were negative
there would also be a reflection across the y-axis. But none
of the answers allows for this.
Here is the graph of
Here is the graph of
You can see that the the second graph has been shrunk horizontally.
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Here is the graph of
Here is the graph of
You can see that the the second graph has been stretched horizontally.
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Here is the graph of
Here is the graph of
You can see that the the second graph has been shrunk horizontally
and reflected across the y-axis.
----------------------------------------
Here is the graph of
Here is the graph of
You can see that the the second graph has been stretched horizontally
and reflected across the y-axis.
Therefore, the correct choice is probably (b), but that does not tell
about the fact that if c is negative there is also a refection across the
y-axis
There is no effect when
There is a horizontal shrink when
There is a horizontal stretch when
There is both a horizontal shrink and a refection across the y-axis when
There is a horizontal stretch and a reflection across the y-axis when
There is only a reflection across the y-axis when
More of these possibilities involve horizontal shrinks and stretches, so
your teacher probably intended for the correct choice to be b.
Edwin