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

Lewis Harvey 2020-12-12 Answered

Explain how you could graph each function by applying transformations.
(a) y=log(x2)+7

(b) y=3logx

(c) y=log(3x)5

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Expert Answer

wheezym
Answered 2020-12-13 Author has 103 answers

(a)
Consider the given function
y=log(x2)+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(x2)
Again, take vertical shift up by 7 units of the above
So,
y=log(x2)+7
Hence, above are the required transformations.
(b)
Consider the given function
y=3logx
To find the transformation of the graph of the given function
yyy===logxlogx (Reflection about the x−axis) 3logx (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

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