Graphing y = 2√(x - 1) + 3

Algebra 1 · Axiom Academy

EXAMPLE Graphing a Radical Function Graph by identifying its transformations of , finding its domain and range, and plotting key points. Graph the radical function . Identify how it is transformed from the parent function , determine its domain and range, and plot three key points. Here is the graph of with the three transformed key points plotted. It starts at (1,3) and rises with the characteristic radical shape. Start point (1, 3) marked first; the curve only exists for and outputs . Nice work — you graphed a transformed radical function. Here is what carries over to any transformation: Read transformations off the equation: a number inside the radical shifts horizontally (and the opposite way), a coefficient out front stretches vertically, and a number added outside shifts vertically. Domain comes from the radicand: set what is under the square root . Here gives . Range comes from the start point: the smallest output is at x = 1 , where y = 3 , so . Transform points with a rule: for , use . The shape is preserved: radical functions always keep that curved shape — only the position and steepness change. The same method works for any function family: spot the inside shift, the outside stretch, and the outside shift, then move a few known points.

This is the written version of the interactive lesson above. See the full Algebra 1 course.