L1.3 A1 Rational Functions - Part 1
Completion requirements
Unit 1
Functions
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Part 1.3A corresponds to section 9.2, starting on page 446 of your Pre-Calculus 12 textbook.
Rational Numbers
Do you like dogs? There are various types of dogs, so even if you do like dogs, you may like Golden Retrievers more than another breed, such as the Pug.Just as there are various categories of dogs, based on size, colour, and disposition, numbers can be put into various categories based on their characteristics as well.
In previous courses, you learned about various types of real numbers.
Rational numbers can be positive or negative and can be written as fractions. Thus, the value of «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«/mstyle»«/math» is rational, and because «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»0«/mn»«mo».«/mo»«mn»5«/mn»«/mstyle»«/math» can be written as «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«/mstyle»«/math», the decimal «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»0«/mn»«mo».«/mo»«mn»5«/mn»«/mstyle»«/math» is also rational. The value «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mo»-«/mo»«mn»25«/mn»«/mstyle»«/math» is rational. It can be written as the fraction «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfrac»«mrow»«mo»-«/mo»«mn»25«/mn»«/mrow»«mn»1«/mn»«/mfrac»«/mstyle»«/math».
The numbers that do not fit in this category are ones that cannot be expressed as a fraction. Additional examples of irrational numbers are «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi mathvariant=¨normal¨»§#960;«/mi»«/mstyle»«/math» and any radical that does not evaluate to a rational value.
«math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«msqrt»«mn»24«/mn»«/msqrt»«mo»=«/mo»«mn»4«/mn»«mo».«/mo»«mn»898979486«/mn»«/mrow»«/mstyle»«/math»… is an example of a radical that evaluates to a decimal value that never repeats or terminates. It is an irrational number.
The numbers that do not fit in this category are ones that cannot be expressed as a fraction. Additional examples of irrational numbers are «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi mathvariant=¨normal¨»§#960;«/mi»«/mstyle»«/math» and any radical that does not evaluate to a rational value.