topic badge

3.03 Evaluating functions


In the lesson Functions and Relations, we were also introduced to the concept of functions, where each input yielded a unique output.

When we are writing in function notation, instead of writing "$y=$y=", we write "$f(x)=$f(x)=". This gives us a bit more flexibility when we're working with equations or graphing as we don't have to keep track of so many $y$ys! Instead, using function notation, we can write $f(x)=$f(x)=, $g(x)=$g(x)=, $h(x)=$h(x)= and so on. These are all different expressions that involve only $x$x as the variable.

We can also evaluate "$f(x)$f(x)" by substituting values into the equations just like we would if the question was in the form "$y=$y=".


Worked example

Question 1

If $f(x)=2x+1$f(x)=2x+1 , find $f(5)$f(5).

Think: This means we need to substitute $5$5 in for $x$x in the $f(x)$f(x) equation.


$f(5)$f(5)  $=$= $2\times5+1$2×5+1
  $=$= $11$11

Reflect: Check the reasonableness of your calculation.  Does it make sense?


Practice questions

Question 2

If $f\left(x\right)=4x+4$f(x)=4x+4,

  1. find $f\left(2\right)$f(2).

  2. find $f\left(-5\right)$f(5).

Question 3

Consider the function $p\left(x\right)=x^2+8$p(x)=x2+8.

  1. Evaluate $p\left(2\right)$p(2).

  2. Form an expression for $p\left(m\right)$p(m).

Question 4

Use the graph of the function $f\left(x\right)$f(x) to find each of the following values.

Loading Graph...

  1. $f\left(0\right)$f(0)

  2. $f\left(-2\right)$f(2)

  3. Find the value of $x$x such that $f\left(x\right)=2$f(x)=2



Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

What is Mathspace

About Mathspace