Functions, Glossary

Knowing the vocabulary of Functions precisely is worth easy marks in SPM Add Math. Questions often turn on a single keyword, read it correctly and the method follows; misread it and even good algebra earns nothing.

Because the SPM paper is bilingual (BM/EN), each term below shows the English and Malay wording, so your child recognises it whichever way a question is phrased.

• Function, A function is a rule that assigns to each input (object) exactly one output (image). We often write it as $f(x)$, for example $f(x)=2x+1$. Every element of the domain must map to a single value, which is what separates a function from a general relation. →
• Domain, The domain of a function is the complete set of all input values (objects) that can be substituted into the function. For $f(x)=\sqrt{x}$ the domain is $x\ge 0$, because negative numbers have no real square root. Choosing a valid domain keeps every output well defined. →
• Codomain, The codomain is the set within which all outputs of a function are declared to lie, before we check which values are actually reached. It is stated when the function is defined, and the range is always a subset of it. Codomain and range need not be equal. →
• Range, The range of a function is the set of all output values (images) that are actually produced when every object in the domain is used. For $f(x)=x^{2}$ with real inputs, the range is $f(x)\ge 0$. It is the part of the codomain that is genuinely reached. →
• Object and Image, In a function $f$, the image is the output value that a particular input produces, written $f(x)$. If $f(3)=7$, then $7$ is the image of the object $3$. Finding an image means substituting a value; finding the object means solving $f(x)=$ that value. →
• Composite Function, A composite function applies one function and then feeds its output into a second function. It is written $fg(x)$ or $(f\circ g)(x)$, meaning do $g$ first, then $f$. Order matters: $fg(x)$ is usually not equal to $gf(x)$, so always work from the inside outwards. →
• Inverse Function, An inverse function $f^{-1}$ reverses a function, sending each image back to its original object, so $f^{-1}(f(x))=x$. Only one-to-one functions have inverses. To find $f^{-1}(x)$, let $y=f(x)$, make $x$ the subject, then swap the letters. →
• Absolute Value Function, The absolute value function $f(x)=|x|$ gives the distance of a number from zero, so its output is never negative. Its graph is V-shaped, formed by reflecting the negative part of the line $y=x$ above the x-axis. This means $|{-4}|=4$ and $|4|=4$. →

Do not just memorise definitions, practise using each term inside a full solution, the way a marker expects to see it. In the Functions chapter especially, stating the right definition or condition in your working can itself earn a method mark.

Our teachers check that a student can both recall a term and deploy it fluently under exam conditions.

Vocabulary sticks best when it is tied to doing rather than reading. Instead of learning the Functions terms as a flat list, meet each one inside a worked question and say the step aloud in words as you write it, a term you can use in a sentence is a term you understand.

It also helps to link related terms together rather than in isolation, since Functions questions usually combine several ideas at once. Because the SPM paper is bilingual, glance once at the Malay and English wording of each term side by side, so the language a question is set in never throws you.

If a term keeps feeling slippery, that is usually a sign the underlying idea needs another look, not the word itself, and that is exactly the kind of gap a one-to-one lesson closes quickly.