Lesson

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 $y$`y`s! 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`=".

If $f(x)=2x+1$`f`(`x`)=2`x`+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?

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

find $f\left(2\right)$

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

`f`(−5).

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

Evaluate $p\left(2\right)$

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

`p`(`m`).

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

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$f\left(0\right)$

`f`(0)$f\left(-2\right)$

`f`(−2)Find the value of $x$

`x`such that $f\left(x\right)=2$`f`(`x`)=2

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