Function Notation and Evaluating Functions
Learn how to use and understand function notation, including evaluating functions for specific values. Explore examples and explanations to enhance your understanding of functions and notation.
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19 April 2025 Function notation LO: To use and understand the notation used for functions. www.mathssupport.org www.mathssupport.org
Functions We sometimes use a function machine to illustrate how functions behave . This function machine has been programmed to perform a particular function First double the number Then add 5 3, 5, 7, 8 . 3 5 7 8 If these numbers are fed into the machine 6 10 14 16 19 21 11, 15, 19, 21 11 These numbers come out 15 If f is used to represent this particular function, we can write f : x 2x + 5 function f such that x is converted into 2x + 5 www.mathssupport.org www.mathssupport.org
Function notation Functions 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 1 y is replaced by f (x) f (x) is read as f of x and means the value of function f at x f (x ) is called the image of x www.mathssupport.org www.mathssupport.org
Function notation An ordered pair (x, y) can be written as (x, f(x)). Another notation. f : x 2x 1 f : x 2x 1 means that fis a function that mapsx to2x 1 We do not always use ffor a function, we can use any other letter. www.mathssupport.org www.mathssupport.org
Evaluating a function Findingf (x) for a particular value of x means evaluating the function f at that value. Example atx = 3 f(x)= 2x 1 f(3)= 2(3) 1 f(3)= 5 Evaluate the function www.mathssupport.org www.mathssupport.org
Evaluating a function findf (0) If f(x)= x2 + 3x 4 f(0)=(0)2+ 3(0) 4 f(0)= 4 www.mathssupport.org www.mathssupport.org
Evaluating a function findf ( 2) If f(x)= x2 + 3x 4 f( 2)=( 2)2+ 3( 2) 4 f( 2)=4 6 4 f( 2)= 6 www.mathssupport.org www.mathssupport.org
Evaluating a function findf (x 1) If f(x)= x2 + 3x 4 (x 1)2 + 3(x 1) 4 f(x 1)= f(x 1)= x2 2x + 1+ 3x 3 4 f(x 1)=x2+ x 6 www.mathssupport.org www.mathssupport.org
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