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Functions (vocabulary (function is a special type of relation. (uploaded…
Functions
vocabulary
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function notation, the symbol f (x) is read f of x and interpreted as the value of the function f at x.
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function’s domain, x is called the independent variable.
range of f is represented by the dependent variable, y.
implied domain is the set of all real numbers for which the expression used to define the function is real.
A function that is defined using two or more equations for different intervals of the domain is called a piecewise-defined function.
examples of the lesson
Describe the set of numbers using set-builder notation.
a. {8, 9, 10, 11, …}
The set includes all whole numbers greater than or equal to 8.
{x | x ≥ 8, x ∈ }
Write each set of numbers using interval notation.
a. −8 < x ≤ 16
(−8, 16]
Determine whether each relation represents y as a function of x
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a. The input value x is a student’s ID number, and the output value y is that student’s score
on a physics exam
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Each value of x cannot be assigned to more than one y-value. A student cannot receive two
different scores on an exam. Therefore, the sentence describes y as a function of x.
State the domain of each function.
g (t) = √t - 5
Because the square root of a negative number cannot be real, t - 5 ≥ 0. Therefore, the domain
of g (t) is all real numbers t such that t ≥ 5 or [5, ∞).
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