SOLUTION: 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 horizo

Algebra ->  Equations -> SOLUTION: 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 horizo      Log On


   

Question 147685: 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)
Found 2 solutions by Nate, Edwin McCravy:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
b.)
For example:
g(x) = 1 / x
g(3x) = 1 / (3x) or g(x/3) = 3 / x

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
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  

g%28x%29+=+log%283%2C%28x%29%29

graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Clog%283%2Cx%29%29

Here is the graph of  

f%28x%29+=+g%282x%29=log%283%2C%282x%29%29%29

graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Clog%283%2C2x%29%29

You can see that the the second graph has been shrunk horizontally.

--------------------------------------------

Here is the graph of  

g%28x%29+=+log%282%2C%28x%29%29

graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Clog%283%2Cx%29%29

Here is the graph of  

f%28x%29+=+g%280.5x%29=log%282%2C%280.5x%29%29

graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Clog%283%2C0.5x%29%29

You can see that the the second graph has been stretched horizontally.

-------------------------------------------------

Here is the graph of  

g%28x%29+=+log%284%2C%28x%29%29

graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Clog%284%2Cx%29%29

Here is the graph of  

f%28x%29+=+g%28-2x%29=log%284%2C%28-2x%29%29

graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Clog%284%2C-2x%29%29

You can see that the the second graph has been shrunk horizontally
and reflected across the y-axis.

----------------------------------------

Here is the graph of  

g%28x%29+=+log%285%2C%28x%29%29

graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Clog%285%2Cx%29%29

Here is the graph of  

f%28x%29+=+g%280.5x%29=log%285%2C%28-0.5x%29%29

graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Clog%285%2C-0.5x%29%29

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 c=1
There is a horizontal shrink when c%3E1
There is a horizontal stretch when 0%3Cc%3C1
There is both a horizontal shrink and a refection across the y-axis when 
c%3C-1
There is a horizontal stretch and a reflection across the y-axis when -1%3Cc%3C0
There is only a reflection across the y-axis when c=-1

More of these possibilities involve horizontal shrinks and stretches, so 
your teacher probably intended for the correct choice to be b.

Edwin