Checking and securing understanding of moving between function notation and the definition | Maths

Starter quiz

A ______ uniquely maps values from the domain to values in the range.

'function' ✓
If $\text{f}(x)= 5x-4$ what is the value of $\text{f}(3)$ ?

'11' ✓
If $\text{g}(x)= x^2- 3x$ what is the value of $\text{g}(4)$ ?

'4' ✓
Expand and simplify $(x+3)^2$ .

$x^2+9$

$x^2 + 3x + 6$

$x^2 + 3x + 9$

$x^2 + 6x + 9$ ✓
Simplify $3(4(2x+1)-5)$ .

$24x-64$

$24x-48$

$24x-3$ ✓

$24x+7$
If $\text{f}(x) = 2x + 4$ and $\text{g}(x) = 3x- 2$ , what is an expression for $\text{fg}(x)$ ?

$5x+2$

$6x$ ✓

$6x-8$

$6x+ 10$

Exit quiz

Match up these manipulations of $\text{f}(x)$ to their definitions.

$\text{f}(x+3)$

⇔

Add 3 to the given value of $x$ then substitute into the function. ✓

$\text{f}(x)+3$

⇔

Evaluate the function for the given value of $x$ then add 3 ✓

$\text{f}(3x)$

⇔

Multiply $x$ by 3 then substitute this value into the function ✓

$3\text{f}(x)$

⇔

Evaluate the function for the given value of $x$ then multiply by 3 ✓
If $\text{g}(x)=3x-5$ match up these manipulation to their value when $x=3$ .

$\text{g}(x+2)$

⇔

$10$ ✓

$\text{g}(x) + 2$

⇔

$6$ ✓

$\text{g}(2x)$

⇔

$13$ ✓

$2\text{g}(x)$

⇔

$8$ ✓
When $\text{f}(x)=2x+4$ which of these is an expression for $\text{f}(x+3)$ ?

$2x+7$

$2x+10$ ✓

$2x+12$

$5x+4$

$5x+7$
When $\text{f}(x)=x^2+4x$ which of these is an expression for $2\text{f}(x)$ ?

$2x^2 + 4x$

$2x^2 + 8x$ ✓

$4x^2 + 4x$

$4x^2 + 8x$
When $\text{f}(x)=5-3x$ which of these is an expression for $2\text{f}(x-4)$ ?

$-6x-14$

$2-6x$

$17-6x$

$34-6x$ ✓
When $\text{f}(x)=2x-x^2$ which of these is an expression for $\text{f}(3x)-2$ ?

$5x-x^2-2$

$5x-9x^2-2$

$6x-x^2-2$

$6x-3x^2-2$

$6x-9x^2-2$ ✓

Worksheet

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Lesson Details

Key learning points

Changing the function changes what it represents
The change in notation can be seen in the algebraic form of the function it represents
If a specific linear function is considered, the effects of this can be seen clearly

Common misconception

A common error is to not substitute into all variable terms where there is more than one in a function. For example, 'Write a simplified expression for f $(x+3)$ when f $(x)=x^2-4x$ '

Use brackets when substituting. For example, for 'Write a simplified expression for f $(x+3)$ when f $(x)=x^2-4x$ ' you would write f $(x+3)=(x+3)^2-4(x+3)$

Keywords

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