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Functions and Function Notation. Highlights. Learning Objectives. In this section, you will: Determine whether a relation represents a function. Find the value of a function. Determine whether a function is one-to-one. Use the vertical line test to identify functions. Graph the functions listed in the library of functions.
f (6) represents the value of the function at x = 6. For the example above, f (x) = 3x + 1 and f (6) = 3 × 6 + 1 = 18 + 1 = 19. Notice that A (s) = s × s is the function notation for the area of a square. The different ways we can read A (s) are: "A of s". "A is a function of s".
Every function has a domain and range. The domain is the set of independent values of the variable x for a relation or a function is defined. In simple words, the domain is a set of x-values that generate the real values of y when substituted in the function.
What is function notation? Function notation is a way of expressing a relationship between two variables. We are used to writing equations of straight lines in the form y = mx + c . Using function notation we can write this as f (x) = mx + c , by replacing y with f (x) .
Function Notation. The notation \(y=f(x)\) defines a function named \(f\). This is read as “\(y\) is a function of \(x\).” The letter \(x\) represents the input value, or independent variable. The letter \(y\), or \(f(x)\), represents the output value, or dependent variable.
function of x. y. =. f (x) Essentially, y is replaced with f (x). In f (x), the f is the name used to identify the given function, while the x is the argument of the function, and describes the input value of the function.
Solution: a) g (a + b) = (a + b) 2 + 2. = a 2 + 2ab + b 2 + 2. b) g (x 2) = (x 2) 2 + 2 = x 4 + 2. Function Notation. Throughout mathematics, we find function notation. Function notation is a way to write functions that is easy to read and understand.
