the graph of[math]f\left(x\right)=\frac{1}{x}[/math] is given above, pls sketch the image of [math]f\left(x\right)[/math]after the two horizontal transformation steps.
Combined Transformation (Part 1)
Recall from revision,
Given that[math]f\left(x\right)=\frac{1}{x},[/math] , the composite functions gives the expression[br][math]g\left(x\right)=2f\left(3\left(x-2\right)\right)-2[/math] [math]=\frac{2}{3\left(x-2\right)}-2[/math][br]What is the order of translation and stretching that will help us obtain the graph of [math]g\left(x\right)[/math] from [math]f\left(x\right)[/math] ?
First let's consider what happens in the bracket of the function (which affects x only)
Which of the following order is correct?[br][br]1. [math]f\left(x\right)=\frac{1}{x}\Longrightarrow h\left(x\right)=f\left(x-2\right)=\frac{1}{x-2}\Longrightarrow[/math]Horizontal translation of 2 units to the right[br]2.[math]p\left(x\right)=h\left(3x\right)=\frac{1}{3x-2}\Longrightarrow[/math] Horizontal stretching of scale factor [math]\frac{1}{3}[/math]
OR [br][br]1.[math]f\left(x\right)=\frac{1}{x}\Longrightarrow h\left(x\right)=f\left(3x\right)=\frac{1}{3x}\Longrightarrow[/math] Horizontal stretching of scale factor[math]\frac{1}{3}[/math] [br]2.[math]p\left(x\right)=h\left(x-2\right)=\frac{1}{3\left(x-2\right)}\Longrightarrow[/math] Vertical translation of 2 units to the right
Hence,