Graphical Transformation of y=ln (x)

[AN630078]

Homework Statement

Hello, I was practising describing graphical transformations with several example questions but there was one which I was especially unsure of. I would appreciate any advice upon my proposed solutions.
Describe the transformation which maps y=ln(x) to;
a. y=ln(2x)
b.y=ln(4-x)

Relevant Equations

y=f(ax) is a horizontal stretch by a scale factor 1/a
y=f(-x) is a reflection in the y-axis
y=f(x+a) is a translation by the vector (-a,0)

a. I believe that y=ln(2x) is a horizontal stretch of y=ln(x) of scale factor 1/2. In the transformation y=ln(2x), each x-value is multiplied by 2 before the corresponding y-value is calculated.

b. I think that y=ln(4-x) is a reflection in the y-axis followed by a translation by the vector (-4,0) i.e. 4 units to the right.

 

[FactChecker]

Just to be clear, you need to say if you are talking about the x-axis being stretched and reflected or about the graph line.

 

[haruspex]

b. I think that y=ln(4-x) is a reflection in the y-axis followed by a translation by the vector (-4,0) i.e. 4 units to the right.

Try reducing that to one operation.

 

[haruspex]

Just to be clear, you need to say if you are talking about the x-axis being stretched and reflected or about the graph line.

If we take the relevant equations as the guide, it must mean a transformation of the curve, keeping the coordinates fixed.

 

[FactChecker]

I would not say that a translation"by the vector (-4,0)" is "4 units to the right." I would say that it is moving the points of the graph line to the left versus the axis system.