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

Explain how you could graph each function by applying transformations.
(a) $y=\mathrm{log}\left(x-2\right)+7$

(b) $y=-3\mathrm{log}x$

(c) $y=\mathrm{log}\left(-3x\right)-5$

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