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Summary Topic III: Real Valued Function
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Covers the following sections: Domain, range, sketching • Manipulating functions • Some common functions: • Powers, polynomials, modulus, logarithms • Exponential growth and decay • Equations: • Simple, quadratic, simultaneous • Differentiation: • Rate of change, finding ma...

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  • February 28, 2024
  • 5
  • 2023/2024
  • Summary

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CSC1031 – Semester 2 Examina3on




Fundamentals Of Computing


Topic III : Real Valued Function


Function – Domain and Range

- Function is a named expression dependent on one or more variables. The variable is also called the

argument of the function.

- The domain of a function f(x) is the set of values for

which it is defined.

- The range or co-domain of a function is the set of all

values that the function can take.




Sketching a function

To sketch a function, we use the x and y axes to represent the domain and range.




Absolute or modulus function




Logarithm

ax = c where a and c are constants

ab =c «b=logac




4

, CSC1031 – Semester 2 Examina3on




Logarithm properties



- loga(x*y) = logax + logay – reducing multiplication to addition

- loga(x/y) = logax – logay – reducing division to subtraction


- loga(xn) = n logax (n can be negative and/or non-integer)

- logax = logbx / logba – can easily change the base

- loga1 = 0


- logaan = n, in particular logaa = 1

logab
- a = b – this is the definition of logarithm




For any natural number n≥1, the number of decimal digits ||n||10 in n is given by:

||n||10 = élog10nù + 1,

where éyù denotes the whole part of y

• E.g. for 1£n<10, ||n||10=1; for 10£n<100, ||n||10=2; etc.

• Thus élog10nù = ||n||10–1, i.e. ||n||10–1 £ log10n < ||n||10

• Generally, the number of digits ||n||k in the base-k representation of n is élogknù + 1, and thus

||n||k–1 £ logkn < ||n||k




5

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