L1.1 A2 Radical Functions - Part 5
Completion requirements
Unit 1
Functions
There is another way the variables in a radical function may be restricted. Contextual variable restrictions exist in certain situations.
For example, the area of a circle is determined using the following formula.
Given the area, the radius can be determined.
Because the variables represent measurements, the restriction on the variable «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«/mstyle»«/math» is that it must be greater than or equal to «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»0«/mn»«/mstyle»«/math».
Always consider the situation being modelled to determine the natural restrictions on a variable in a function.
For example, the area of a circle is determined using the following formula.
«math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«msub»«mi»A«/mi»«mi»circle«/mi»«/msub»«mo»=«/mo»«mo»§#960;«/mo»«msup»«mi»r«/mi»«mn»2«/mn»«/msup»«/mrow»«/mstyle»«/math»
Given the area, the radius can be determined.
«math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»r«/mi»«mo»=«/mo»«msqrt»«mfrac»«msub»«mi»A«/mi»«mi»circle«/mi»«/msub»«mo»§#960;«/mo»«/mfrac»«/msqrt»«/mrow»«/mstyle»«/math»
Because the variables represent measurements, the restriction on the variable «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«/mstyle»«/math» is that it must be greater than or equal to «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»0«/mn»«/mstyle»«/math».
Always consider the situation being modelled to determine the natural restrictions on a variable in a function.
