3.4.4 A linear function

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3.4.4 A linear function

Another example to convince you that you have dealt with functions even if you are not aware of it is the conversion of temperatures. For example, to convert from Centigrade to Fahrenheit you use the simple rule (function) ``multiply by 9/5 and then add 32''. If a function only involves multiplication and addition it is termed a linear function.

You can see that this example is a combination of the previous 2. It involves a multiplication step ( $\times$ 9/5) and then the addition of a constant (32).

Graphically, we have :

$\begin{picture}(8,8) \put(1,4){\vector(1,0){7}} \put(1,5){ \textcolor{blue}{Degr... ...tor(1,0){6}} \put(14.5,5){ \textcolor{green4}{Degrees Fahrenheit}} \end{picture}$

Expressed as a function we have,

$\begin{picture}(8,8) \put(1,4){\vector(1,0){7}} \put(5,5){\textcolor{blue}{ $x$ ... ...\put(14,4){\vector(1,0){6}} \put(18,5){ \textcolor{green4}{$y$ } } \end{picture}$

where b= 32 and $m=\frac{9}{5}$ .

For example, we can see how the rule takes as an input 20 degrees centigrade and converts it to Fahrenheit:

$\begin{picture}(8,8) \put(1,4){\vector(1,0){7}} \put(5,5){\textcolor{blue}{20}} ... ...}}} \put(14,4){\vector(1,0){6}} \put(18,5){\textcolor{green4}{68}} \end{picture}$

Next: 3.4.5 The function as Up: 3.4 Examples of functions Previous: 3.4.3 The function as

Richard Waterman
1999-04-30