LO To use and understand the notation used for functions 3 5 7 8 Functions 11 15 19 21 3 11 We sometimes use a function machine to illustrate how functions behave ID: 1047441
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1. 26 July 2022Function notationLO: To use and understand the notation used for functions.
2. 3, 5, 7, 8 ….Functions11, 15, 19, 21311We sometimes use a function machine to illustrate how functions behave .These numbers come out515719821×2+56101416This function machine has been programmed to perform a particular functionFirst double the numberThen add 5If these numbers are fed into the machineIf f is used to represent this particular function, we can writef : x↦ 2x + 5function fsuch thatxis converted into2x + 5
3. Function notationf (x) is read as ‘f of x’ and means the value of function f at xis called the image of xFunctions are often described by equations.For example, the equation y = 2x – 1 describes y as a function of x.By giving the function the symbol f we write this equation in function notation as. f (x) = 2x – 1y is replaced by f (x)
4. Another notation.f : x 2x – 1An ordered pair (x, y) can be written as (x, f(x)).We do not always use f for a function, we can use any other letter.f : x 2x – 1 means that f is a function that maps x to 2x – 1Function notation
5. Evaluating a functionFinding f (x) for a particular value of x means evaluating the function f at that value. f (x) = 2x – 1Evaluate the functionat x = 3f (3) = 2(3) – 1f (3) = 5Example
6. f (x) = x2 + 3x – 4If find f (0)f (0) = (0)2 + 3(0) – 4f (0) = –4 Evaluating a function
7. f (x) = x2 + 3x – 4If find f (–2)f (–2) = (–2)2 + 3(–2) – 4f (–2) = – 6 f (–2) = 4 – 6 – 4 Evaluating a function
8. f (x) = x2 + 3x – 4If find f (x – 1)(x–1)2f (x–1) = x2 + x – 6x2 – 2x + 1+ 3x – 3– 4+ 3(x–1)– 4f (x–1) =f (x–1) =Evaluating a function
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