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
asked 2020-12-12

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

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

(c) \(y = \log(-3x)-5\)

Answers (1)

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

0
 
Best answer

expert advice

Need a better answer?
...