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How to Graph a Transformation of a Square Root Equation

A function is a mathematical machine that takes a given input and generates an output. There are many different types of functions in mathematics, including trigonometric functions, power functions and inverse power functions. The square root function is an example of an inverse function, and its graph has a steep slope to start with that decreases with increasing x value. Graphs can be transformed so their features move relative to the x and y axis. This is generally a simple task to achieve.

Things You'll Need

Graph paper

Instructions

- 1
  Decide upon the transformation. An arbitary function can be transformed using the following rules. In order to shift the graph in the x direction, you use f(x+t) where t is the shift in the graph. In order to shift the graph in the y direction you use f(x)+y where y is the shift in the graph. For example to shift the square root function to the right by 1 and up by 2, the following equation would be used: y= (SQRT(x-1) ) + 2
- 2
  Make a table of the graph to determine some key values. Following the example:
  
  x=1 x+1=2 (SQRT(x+1) ) + 2=3.41
  
  x=2 x+1=3 (SQRT(x+1) ) + 2= 3.73
  
  x=3 x+1=4 (SQRT(x+1) ) + 2= 4
- 3
  Plot the values for x along the x axis and the values for (SQRT(x+1) ) + 2 along the y axis. The graph should be translated to the right by 1 unit and up by 2 units.

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