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MATH137 lecture notes.pdf

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MATH 137
Conrad Hewitt

Math137 Lecture Notes Erin Edward Introduction: A course in single real variables using the universal set of R (real numbers) *also sets of 𝐑 and 𝑹 *𝟑 x R where x is the number of variables How do we provide a function?  Verbally – in words  Numerically – set of values  Visually – graph  Algebraically – formula Visually and algebraically are the most useful Functions: Subsets of R: We will have a function, F: A→B, where the components are elements of R (real numbers), making the function a subset of R Ex: Let a, b ER a output (y) REMARK: Vertical line test A curve is a function if all vertical lines intersect the curve at most once Reason – the function is single valued If not a functions, split the curve into two parts to work with (restrict the range) OR switch the x and y values (the inverse) Ex: y=G(x) X=G(y) INCREASING AND DECREASING FUNCTIONS Math137 Lecture Notes Erin Edward Ex: F: I→B We say that: 1. F is increasing on I to mean that F(x )>F(x 1 for 2ll x , x E1 wi2h x >x 1 2 2. F is non-decreasing on I to mean that F(x )≥F(x ) 1or all2x , x EI w1th 2 >x
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