A function is a rule made of one or more operations that turns a set of numbers into another set of numbers. The numbers put in are the inputs and the numbers coming out are the outputs .

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Functions (SQA National 5 Maths): Flashcards

Exam code: X847 75

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FrontFunction Notation f(x)
Define a function.

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Cards in this collection (8)

Define a function.
A function is a rule made of one or more operations that turns a set of numbers into another set of numbers.
The numbers put in are the inputs and the numbers coming out are the outputs.
In $f (x) = 2 x + 1$ what is the input and what is the output?
$x$ is the input and $f (x)$ is the output, so the notation names the rule and the number going into it at the same time.
Letters other than $f$ can be used, with $g$ , $h$ and $j$ all common.
How is $f (6)$ evaluated when $f (x) = 4 x + 5$ is given?
Substitute $6$ into the expression everywhere an $x$ appears, giving $f (6) = 4 (6) + 5$ .
Working that out gives $f (6) = 29$ .
Complete the working for the function $f (x) = 2 x + 1$ by filling in the two missing values.
$f (- 4) = 2 \times (______) + 1 =______$
The completed working is:
$f (- 4) = 2 \times (- 4) + 1 = - 7$
Keeping the $- 4$ inside brackets while multiplying is what stops the sign being lost.
True or False?
$f (t + 5)$ means $f$ multiplied by $t + 5$ .
False.
The brackets in function notation show the input, so $f (t + 5)$ is the output when $t + 5$ is put into the function.
Nothing is being multiplied, so it does not equal $f t + 5 f$ .
In what way do $f (x) = 15$ and $f (15)$ mean different things?
$f (x) = 15$ says the output is $15$ , so an equation has to be solved to find the input.
$f (15)$ says the input is $15$ , so you substitute and work out the output.
True or False?
Putting a letter rather than a number into a function gives an answer that still contains that letter.
True.
A function carries out the same operations whatever goes in, so $f (x) = 2 x + 1$ gives $f (a) = 2 a + 1$ .
The answer stays in terms of $a$ because there is no number to work out.
If the output of a function is known how do you find the input?
Replace $f (x)$ with the rule of the function, set that equal to the known output, and solve the resulting equation.
For $f (x) = 2 x + 1$ with an output of $15$ the equation is $2 x + 1 = 15$ , giving an input of $x = 7$ .

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