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Extra info for An elementary treatise on cubic and quartic curves
X ϭ the directed distance from the y-axis f ͑x͒ ϭ the directed distance from the x-axis Example 1 shows how to use the graph of a function to find the domain and range of the function. Example 1 Finding the Domain and Range of a Function Find the domains and ranges of functions and use the Vertical Line Test for functions. Determine intervals on which functions are increasing, decreasing, or constant. Determine relative maximum and relative minimum values of functions. Identify and graph step functions and other piecewise-defined functions.
Answer: No 3 . xϩ1 Answer: All real numbers x except x ϭ Ϫ1 0 Now try Exercise 93. Summary of Function Terminology Function: A function is a relationship between two variables such that to each value of the independent variable there corresponds exactly one value of the dependent variable. Function Notation: y ϭ f ͑x͒ f is the name of the function. y is the dependent variable, or output value. x is the independent variable, or input value. f ͑x͒ is the value of the function at x. Domain: The domain of a function is the set of all values (inputs) of the independent variable for which the function is defined.
A review of radical functions can be found in the Study Capsules. Graph of f ͑x͒ ϭ Ίx y Domain: ͓0, ϱ͒ Range: ͓0, ϱ͒ Intercept: ͑0, 0͒ Increasing on ͑0, ϱ͒ 4 3 f(x) = x 2 1 −1 x −1 (0, 0) 2 3 4 STUDY TIP Because the square root function is not defined for x < 0, you must be careful when analyzing the domains of complicated functions involving the square root symbol. 2 21 Functions Example 5 Finding the Domain of a Function Find the domain of each function. a. f : ͭ͑Ϫ3, 0͒, ͑Ϫ1, 4͒, ͑0, 2͒, ͑2, 2͒, ͑4, Ϫ1͒ͮ b.