Defining function notation | Maths | Quizalize & Oak National Academy

Starter quiz

A function is a mathematical relationship that uniquely __________ values of one set to the values of another set.

maps ✓

transfers

substitutes

ages
Match the expression to the description of each function.

$3x+7$

⇔

$x$ is multiplied by $3$ then $7$ is added. ✓

$3(x+7)$

⇔

$7$ is added to $x$ then the sum is multiplied by $3$ ✓

$3x-7$

⇔

$x$ is multiplied by $3$ then $7$ subtracted ✓

$7-3x$

⇔

$x$ is multiplied by $3$ then subtracted from $7$ ✓

$7(3-x)$

⇔

$x$ is subtracted from $3$ , then the result is multiplied by $7$ ✓

$7(x-3)$

⇔

$3$ is subtracted from $x$ , then the result is multiplied by $7$ ✓
When graphing the linear equation $y=7x+9$ what is the value of the $y$ coordinate when $x=5$ ?

'44' ✓
When graphing the linear equation $y=7x+9$ what is the value of the $y$ coordinate when $x=-5$ ?

$44$

$26$

$-26$ ✓

$-44$
When graphing the equation $y=10-x^2$ what is the value of the $y$ coordinate when $x=-3$ ?

$19$

$1$ ✓

$-1$

$-19$

$-13$
Which of the below are invalid inputs into the equation $6\over{x^2+x-20}$ ?

$x=20$

$x=0$

$x=-1$

$x=4$ ✓

$x=-5$ ✓

The __________ of a function is the set of values mapped to by the function and the stated domain.

output

range ✓

domain

input
Instead of writing 'the function $5x-8$ ' we would write it using the shorthand notation ...

$5{\text{f}}(x)-8$

${\text{f}}=5x-8$

${\text{f}}x=5x-8$

${\text{f}}(x)=5x-8$ ✓

${\text{f}}(x)+5x-8$
If ${\text{f}}(x)=12-5x$ then ${\text{f}}(3)=$ ______.

'-3' ✓
If ${\text{f}}(x)=12-5x$ evaluate ${\text{f}}(-2)$ .

$22$ ✓

$2$

$-2$

$-22$
If ${\text{f}}(x)=5x+12$ evaluate $7{\text{f}}(4)$ ______

'224' ✓
If ${\text{f}}(x)=5x+12$ and ${\text{g}}(x)=2-3x$ evaluate ${\text{f}}(4)-{\text{g}}(3)$ ______

'39' ✓

Loading worksheet ...

Loading presentation ...

There is a shorthand for writing a function.
The notation means that the whole function does not need to be written out each time.
The notation should always be defined at the start.
It is possible to substitute the notation for the function it represents.

Pupils may confuse the domain and the range.

Drawing the graph of the function and labelling the axes correctly will help pupils connect domain and range.

Function - A function is a mathematical relationship that uniquely maps values of one set to the values of another set.
Domain - The domain of a function is the set of values that the mapping is performed on.
Range - The range of a function is the set of values mapped to by the function and the stated domain.