Foundation and Higher · functions
Functions.
Number in,
number out.
f(4) does not mean
f times 4
a function is —
A rule
one input gives one output
written as a machine or as f(x)
step 1 of 4
A function machine
1. Put a number in on the left.
2. Follow the rule one box at a time.
✓ 4 × 2 = 8, then 8 + 3 = 11
the function: × 2, then + 3
step 2 of 4
Function notation
1. f(x) is the rule written in algebra.
2. f(4) means: put 4 in place of x.
✓ f(4) = 11
f(x) = 2x + 3 the same machine
f(4) = 2 × 4 + 3
f(4) = 11
step 3 of 4
A negative input
1. Brackets around the negative.
2. 2 × (−5) = −10. Then add 3.
✓ f(−5) = −7
f(x) = 2x + 3
f(−5) = 2 × (−5) + 3
= −10 + 3
= −7
step 4 of 4
Work backwards
1. This time you know the output.
2. Set the rule equal to 15, then solve.
✓ x = 6. Check: 2 × 6 + 3 = 15
f(x) = 15 find x
2x + 3 = 15
2x = 12 − 3
x = 6 ÷ 2
function notation —
f(4) is not f × 4.
It means: the output when x is 4.
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