{"id":218,"date":"2017-05-15T01:29:13","date_gmt":"2017-05-14T19:59:13","guid":{"rendered":"http:\/\/ibelitetutor.com\/blog\/?p=218"},"modified":"2025-05-27T00:50:05","modified_gmt":"2025-05-26T19:20:05","slug":"ib-mathematics-domain-range-function","status":"publish","type":"post","link":"https:\/\/ibelitetutor.com\/blog\/ib-mathematics-domain-range-function\/","title":{"rendered":"IB Mathematics (part-2)-Domain and Range of a function"},"content":{"rendered":"

For IB Maths Tutors<\/a> <\/strong>both HL and SL, functions are one of the most important areas because they lie at the heart of much of mathematical analysis.here I am discussing domain and range of a function<\/p>\n

Domain of a Function<\/strong><\/p>\n

Suppose I say that f is a real function.This means that for real input, the output should be real. For example<\/p>\n

\u00a0F(x)=\u221ax<\/strong><\/p>\n

if F<\/strong> is real, then x can only take non-negative values because only then the output will be real. Set of all real values of R is called domain<\/p>\n

\u201cDomain is the set of all possible inputs for which the output is real \u201d<\/strong><\/p>\n

In some cases, x is defined explicitly. for example,<\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0y=f(x<\/strong>)<\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0=x\u00b2<\/strong>; \u00a0 \u00a01<x>2<\/strong> here domain is defined explicitly as (1,2)<\/strong><\/p>\n

If no domain is mentioned explicitly, the domain will be assumed to be such that “F” produces real output<\/p>\n

These are a few examples<\/p>\n

    \n
  1. y=f(x)=\u221ax<\/strong>
    \nDomain D= x\u22650<\/strong><\/li>\n<\/ol>\n

    <\/p>\n

    2) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 f(x)=\u221ax \u00a0 \u00a0<\/strong><\/p>\n

    Domain \u00a0 D= 2\u2220x\u22643\u00a0\u00a0<\/strong>\u00a0\u00a0\u00a0 or\u00a0\u00a0\u00a0\u00a0 x\u2208(2,3)<\/strong><\/p>\n

    3) \u00a0 \u00a0 \u00a0 \u00a0 y=1\u2215x<\/strong> \u00a0then domain will be any real number excluding zero<\/p>\n

    Domain D=<\/strong>\u211d-{0}<\/strong><\/p>\n

    4) \u00a0 \u00a0 \u00a0 \u00a0y=logx <\/strong>\u00a0then the domain will be any positive integer because logs are only defined for positive real numbers<\/p>\n

    \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D=x\u22651<\/strong>
    \nRange of a function-<\/strong> It is simply the set of possible outputs for a defined domain.<\/p>\n

    Range depends upon domain
    \nExamples:<\/p>\n

    1)\u00a0 y=x\u00b2<\/strong><\/p>\n

    Domain \u00a0x=\u211d<\/strong><\/p>\n

    Range \u00a0 \u00a0y\u22650<\/strong><\/p>\n

    2) \u00a0y=\u221ax<\/strong><\/p>\n

    Domain x\u22650<\/strong><\/p>\n

    Range \u00a0 \u00a0y\u22650<\/strong><\/p>\n

    3) \u00a0y=\u221ax \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a02\u2220x\u22643<\/strong><\/p>\n

    Domain \u00a0x=(2,3)<\/strong><\/p>\n

    Range \u00a0 \u00a0 y=(\u221a2,\u221a3)
    \n<\/strong><\/p>\n

    Question asked in IB Mathematics are usually more complex than above examples
    \n<\/strong><\/p>\n

    To have a graphical picture in mind, consider this image<\/p>\n

    \"<img
    visual of a function by ib elite tutor<\/figcaption><\/figure>\n

    When plotted on a graph, the independent variable (x) is plotted on the horizontal axis while the dependent variable (y) is plotted on vertical axis<\/p>\n

    \"img
    graph of a function to find its domain and range<\/figcaption><\/figure>\n

    Suppose y<\/strong> depends on x<\/strong> as shown in above figure. You can easily tell the domain and range of the function just by looking at the above figure.
    \nDomain D=a\u2264x\u2264b<\/strong> or<\/p>\n

    \u00a0 D=[a,b]\u00a0<\/strong><\/p>\n

    look along the y<\/strong> axis and we see that the graph only varies only between certain values of y<\/strong><\/p>\n

    so Range R=c\u2264x\u2264d or<\/p>\n

    R=[c,d]<\/p>\n

    To summarise, for domain look along x-axis, for range look along y-axis<\/strong><\/p>\n

    It’s practice time now :)-<\/h4>\n

    Try these questions and find domain and range of a function.pdf<\/span><\/h4>\n

    In my next article on IB Mathematics, I will discuss various types of functions<\/p>\n

    \"ib<\/p>\n\n

    \n

    <\/p>

      <\/ul><\/div>\n
      \n
      \n<\/fieldset>\n

      \n<\/p>

      <\/div>\n<\/form>\n<\/div>\n\n

       <\/p>\n","protected":false},"excerpt":{"rendered":"

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