Graph the function using transformation g(x)=-4|x|+1

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embizze eNotes educator| Certified Educator

The basic transformations to the graph of `f(x)` (the base function) if the transformed function is `Af(x-h)+k` are:

A: performs a vertical stretch/compression. If A<0 then the function is reflected over the horizontal axis.

h: performs a horizontal translation

k: performs a vertical translation

In this case, the base function is the absolute value function `y=|x|` ; A=-4,h=0, and k=1. Thus there is a vertical stretch of factor 4, the graph is reflected over the x-axis, and then the graph is vertically translated 1 unit up.

** The vertex of the transformed graph will be at (0,1); the graph opens down, and is narrower than the base function **

The graph: `y=|x|` in black, `y=4|x|` in blue, `y=-4|x|` in green, and the final transformation `y=-4|x|+1` in red