F(x) = |2x-1| +3; reflected across the y axis

Question

Algebra 2 translating graphs 

Answer 1

To reflect about the y-axis, negate x.

f(x) = |2x - 1| + 3

 

Let g be the reflection.

g(x) = |2(-x)-1| + 3 = |-2x - 1| + 3 

Answer 2

A reflection across the y-axis is a horizontal shift.  This of F(x) as the graph of   f(x)=|x|   that stretches vertically by factor of 2 and shifts horizontally to the right unit.  So the reflection of F(x) would be

 

G(x) = | 2x + 1 | + 3