Checking and securing understanding of function notation | Maths

Starter quiz

When graphing the linear equation $y=6x-10$ , what is the value of the $y$ coordinate when $x=3$ ?

'8' ✓
When graphing the linear equation $y=6x-10$ , what is the value of the $y$ coordinate when $x=-1$ ?

'-16' ✓
Match these key words to their definitions.

domain

⇔

the set of values for a function that the mapping is performed on ✓

function

⇔

a relationship which uniquely maps values in one set to another ✓

inverse function

⇔

a relationship which reverses the mapping of the original function ✓

range

⇔

the set of values mapped to, by the function ✓
When we graph the equation $y= x^2$ , what is the minimum value (i.e. the smallest value of the $y$ coordinate)?

'0' ✓
Which of these is not a valid input for $x$ in the equation $y = \frac{1}{2x}$ ?

-2

-1

0 ✓

1

2
What does $\text{sin}^{-1} (x)$ mean?

"sine of -1"

"sine multiplied by -1"

"1 divided by $\text{sin}(x)$ "

"sine inverse of $x$ " ✓

" $\text{sin}(x)$ to the power of -1"

Exit quiz

If $\text{f}(x)= 4(x-2)$ , which is the correct notation for the inverse function $\text{f}$ inverse of $x$ ?

$\text{f}(-1)= \frac{x}{4} + 2$

$-\text{f}(x)= \frac{x}{4} + 2$

$\text{f}^{-1}(x)= \frac{x}{4} + 2$ ✓

$\text{f}(x)^{-1}= \frac{x}{4} + 2$
If $\text{g}(4) = 6$ , then $\text{g}^{-1}(6) =$ ______.

'4' ✓
If $\text{f}(x)= 3x - 5$ , $\text{g}(x)= 10-2x$ and $\text{h}(x)= x^2 + 3$ . Match up these functions with their outputs.

$\text{f}(-2)$

⇔

$-11$ ✓

$\text{g}(-2)$

⇔

$14$ ✓

$\text{h}(-2)$

⇔

$7$ ✓

$\text{f}(1)$

⇔

$-2$ ✓

$\text{g}(1)$

⇔

$8$ ✓

$\text{h}(1)$

⇔

$4$ ✓
Which is the correct range for $\text{f}(x)= x^2 + 4$ with the domain { $x$ : $x$ is any value}?

{ $\text{f}(x) : \text{f}(x) > 4$ }

{ $\text{f}(x) : \text{f}(x) \ge 4$ } ✓

{ $\text{f}(x) : \text{f}(x) < 4$ }

{ $\text{f}(x) : \text{f}(x) \le 4$ }
Which is the correct range for $\text{f}(x)= \text{sin}(x)$ with the domain { $x : 0 \le x \le 180$ }?

{ $\text{f}(x) : 0 \le \text{f}(x) \le 0$ }

{ $\text{f}(x) : 0 \le \text{f}(x) \le 1$ } ✓

{ $\text{f}(x) : -1 \le \text{f}(x) \le 1$ }

{ $\text{f}(x) : -1 \le \text{f}(x)\le 0$ }
Which domain restrictions would make $\text{f}(x)= \frac{24}{x}$ a valid function?

$\text{f}(x)= \frac{24}{x}$ when { $x : x > 0$ } ✓

$\text{f}(x)= \frac{24}{x}$ when { $x : x \ge 0$ }

$\text{f}(x)= \frac{24}{x}$ when { $x : x < 0$ } ✓

$\text{f}(x)= \frac{24}{x}$ when { $x : x \le 0$ }

$\text{f}(x)= \frac{24}{x}$ when { $x : x \not= 0$ } ✓

Worksheet

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Video

Lesson Details

Key learning points

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

Common misconception

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.

Keywords

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.
Inverse function - An inverse function reverses the mapping of the original function.