(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
Explain how you could graph each function by applying transformations.(a) y = log(x -2) + 7 (b) y = -3logx (c) y = log(-3x)-5
Answers (1)
Relevant Questions
Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.
\(y=\sqrt{x - 2} - 1\)
Create a new function in the form \(y = a(x- h)^2 + k\) by performing the following transformations on \(f (x) = x^2\)
Give the coordinates of the vertex for the new parabola.
h(x) is f (x) shifted right 3 units, stretched by a factor of 9, and shifted up by 7 units. \(h(x) = ?\)
Edit Coordinates of the vertex for the new parabola are:
\(x=?\)
\(y =?\)
Graph by labeling three points and determine the type or types of transformations:
\(h(x)=\sqrt{x-2}-1\)
Your friend attempted to describe the transformations applied to the graph of \(y=\sin x\) to give the equation \(f(x)=\frac{1}{2} \sin(-\frac{1}{3}(x+30))+1\).
They think the following transformations have been applied. Which transformations have been identified correctly, and which have not? Justify your answer.
a) f(x) has been reflected vertically.
b) f(x) has been stretched vertically by a factor of 2.
c) f(x) has been stretched horizontally by a factor of 3.
d) f(x) has a phase shift left 30 degrees.
e) f(x) has been translated up 1 unit.
