# The graph of the function g is formed by applying the indicated sequence of transformation to the given function f. Find the function g: a) The graph of f(x)= absolute value of x is reflected about...

The graph of the function g is formed by applying the indicated sequence of transformation to the given function f. Find the function g:

a) The graph of f(x)= absolute value of x is reflected about the x-axis, vertically shrunk by a factor of .5, shifted 3 units to the right and shifted 2 units down.

b) The graph of f(x)= cube root of x is shifted four units to the left and two units down. For this one I got f(x)= (cube root of x +4) -2 .. is that correct?

rcmath | High School Teacher | (Level 1) Associate Educator

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A) When you reflect abs(x) about the x-axis, you end up with -abs(x).

Next let's pay attention to the fact that when yo multiply by 0.5 the graph actually expand and not shrink. So for it to shrink by half means to multiply by 2.
Shift to the right 3 means subtract 3 from x, and 2 up, you add 2 to the function. Thus we end up with

`y=2lx-3l+2` (that is 2*abs(x-3)+2)