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Question # Explain how you could graph each function by applying transformations.(a) y = log(x -2) + 7 (b) y = -3logx (c) y = log(-3x)-5

Performing transformations
ANSWERED Explain how you could graph each function by applying transformations.
(a) $$y = \log(x -2) + 7$$

(b) $$y = -3\log x$$

(c) $$y = \log(-3x)-5$$ 2020-12-13

(a)
Consider the given function
$$y=\log(x−2)+7$$
To find the transformation of the graph of the given function
First, draw the graph of the following function
$$y=\log(x)$$
Now, take horizontal shift right 2 units of the above
So,
$$y=\log(x−2)$$
Again, take vertical shift up by 7 units of the above
So,
$$y=\log(x−2)+7$$
Hence, above are the required transformations.
(b)
Consider the given function
$$y=−3 \log x$$
To find the transformation of the graph of the given function
$$yyy=== \log x −\log x$$ (Reflection about the x−axis) $$−3 \log x$$ (Dilation with scale factor 3 −stretched vertical)
Hence, the required transformations for the graph of the given function are reflection and dilation.
(c)
Consider the given function
$$y= \log (−3x)−5$$
To find the transformation of the graph of the given function
$$y= \log (x)y= \log (3x)$$ (Dilation by scaling factor 3−stretched horizontal)$$y= \log (−3x)$$ ( Reflection about the y−axis )$$y= \log (−3x) −5$$ (Vertical shift down 5 units )
Hence, the required transformations for the graph of the given function are dilation by scaling factor 3 units, reflection about the y-axis, and vertical shift down 5 units