Evaluating Functions Revision Notes for Leaving Cert Mathematics

Evaluating Functions

To evaluate a function means to calculate the output value of the function for a given input value. In other words, you substitute a specific number (or expression) into the function and perform the operations defined by the function.

Suppose our function is defined as $f(x)=2x+3$ . If you are asked to evaluate $f(4)$ , replace $x$ with $4$ in the function :

f(4)=2(4)+3

Evaluate the calculation :

2(4)+3=11

Therefore, when we input $4$ into the function, the output is $11$ . $x$ can be seen as a general placeholder for whatever input we wish to put into our function.

Example

infoNote

If $f(x)=3x+5$ , evaluate $f(a+2)$ .

Wherever we see an $x$ , replace it with the input, $(a+2)$ :

f(a+2)=3(a+2)+5

Simplify the expression :

3(a+2)+5= 3a+6+5=3a+11

Therefore, $f(a+2)=3a+11$

Evaluating Functions (Leaving Cert Mathematics): Revision Notes