Checking and securing understanding of functions | Maths

Starter quiz

$4(x-8) - x + 3$ is an example of...

an expression. ✓

an equation.

an algebraic equation.

an algebraic term.
When graphing the linear equation $y=5x-8$ what is the value of the $y$ coordinate when $x=3$ ?

'7' ✓
When graphing the linear equation $y=5x-8$ what is the value of the $y$ coordinate when $x=-1$ ?

$3$

$13$

$-13$ ✓

$-3$
When we graph the equation $y=8 - x^2$ what is the maximum value (i.e. the largest value of the $y$ coordinate)?

$8$ ✓

$2$

$0$

$-2$

$-8$
$x=7$ is not a valid input for which of these equations?

$y={3\over7x}$

$y={3\over{x+7}}$

$y={3\over{x-7}}$ ✓

$y={x-7\over{3}}$

$y={3\over{4(x-7)}}$ ✓
Which $x$ values cannot be input into the equation $y={x+2\over{(x-3)(x+5)}}$ ?

$-2$

$-3$

$-5$ ✓

$3$ ✓

$5$

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

An equation

A function ✓

An expression

An algebraic term
When graphing functions the $x$ values are the domain and the $y$ values are the ______.

'range' ✓
Which of these values belong to the range, but not the domain, of the function $x^2+5$ ?

$5$

$-5$

$25$

$-25$

None of these values belong only to the range. ✓
Which of these values belong to the domain, but not the range, of the function $5-x^2$ ?

$5$

$-5$

$25$ ✓

$-25$

All of these values will be in the range of the function $5-x^2$
On which of the below would we need to restrict the domain in order to make the function valid?

$y=-9x$

$y={9\over{x}}$ ✓

$y=-{x\over{9}}$

$y={1\over{(x+9)}}$ ✓
Which of these are many-to-one functions?

$y=4x$

$y=4x^2$ ✓

$y=4x^3$

$y=4x^3+4x^2$ ✓

$y=4x^3-4x^2$ ✓

Loading worksheet ...

Loading presentation ...

A function has a set of inputs and outputs.
For any valid input, there is an output.
A function takes an input and performs a series of operations, leading to an output.
The set of inputs is called the domain.
The set of outputs is called the range.

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.