katherinesmith
  • katherinesmith
The red graph (1) is the graph of f(x) = log(x). Describe the transformation of the blue function (2) and write the equation of the graph.
Mathematics
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SOLVED
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chestercat
  • chestercat
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katherinesmith
  • katherinesmith
1 Attachment
katherinesmith
  • katherinesmith
reflection across the x-axis
phi
  • phi
and then a shift down

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phi
  • phi
if you first reflect the red curve, the y=+1 on the right side of the curve becomes y=-1 then it looks like you shift down a little more to get to the blue curve.
katherinesmith
  • katherinesmith
so how many units down is the shift
katherinesmith
  • katherinesmith
3?
phi
  • phi
look at the point (10,1). multiply the y value by -1 to reflect the point you get (10,-1) the blue curve is at (10,-4) so you shift down 3
katherinesmith
  • katherinesmith
yay that's what i thought
phi
  • phi
and there is no right/left shift.
katherinesmith
  • katherinesmith
correct. so how do i write in an equation that the graph reflected and shifted down 3 units
phi
  • phi
first multiply the original by -1, then add -3 to shift down (just like usual)
katherinesmith
  • katherinesmith
f (x) = log(-1) -3 is that right?
phi
  • phi
the -3 is ok you start with f(x)= log(x) if you make it f(x)= -log(x) that will reflect it (the y values become negative)
katherinesmith
  • katherinesmith
gotcha, so f(x) = -log(x) -3 ?
phi
  • phi
yes
katherinesmith
  • katherinesmith
thank god. only one left!
phi
  • phi
btw, you can't take log of negative numbers
katherinesmith
  • katherinesmith
i think i knew that. hahaha
katherinesmith
  • katherinesmith
i'll open a new question

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