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.
Do:
| $f(5)$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,
find $f\left(2\right)$f(2).
find $f\left(-5\right)$f(−5).
Question 3
Consider the function $p\left(x\right)=x^2+8$p(x)=x2+8.
Evaluate $p\left(2\right)$p(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.
$f\left(0\right)$f(0)
$f\left(-2\right)$f(−2)
Find the value of $x$x such that $f\left(x\right)=2$f(x)=2