Analyzing f(x) = 2√(x - 3) + 1

Algebra 2 · Axiom Academy

Building step-by-step from the parent function . Describe as a sequence of transformations of the parent function , then determine its domain, range, and starting point. Excellent work — you've analyzed every transformation that builds . Here's what to carry forward: Order matters: start with the parent function and apply each transformation systematically, one at a time. Inside vs. outside: a change INSIDE the radical, like (x-3) , affects horizontal position; changes OUTSIDE, like and +1 , affect vertical position. Domain shifts with horizontal transformations: shifting right by 3 changed the domain from to . Range shifts with vertical transformations: the vertical stretch left the range starting at 0 , but the +1 shift moved it to . Starting point: the starting point of the graph moved from (0,0) to (3,1) . For any square root function, find the starting point by setting the expression inside the radical equal to zero, then apply the vertical stretch and shift to get the corresponding y -value.

This is the written version of the interactive lesson above. See the full Algebra 2 course.