Some typical assignments related to the domain and range of functions:
Find the domain and range of the following functions: a) f(x) = √(x – 3) b) g(x) = 1/(x^2 – 4) c) h(x) = |2x + 5|
Determine if the following relations represent functions. If so, find their domains and ranges: a) {(x, y) | y = x^2, x is an integer} b) {(x, y) | x^2 + y^2 = 25}
Given the graph of a function, How to identify the domain and range from the graph?
Write the domain and range in interval notation for the following functions: a) f(x) = (x^2 – 9)/(x – 3) b) g(x) = 2^x
Explain the differences between natural domain, domain of definition, and practical domain for a function. Give examples of each.
Prove or disprove: If f(x) is a polynomial function, then its domain is all real numbers.
Find the domain of the function f(x) = (x^2 – 4)/(x – 2). Describe the behavior of the function at the points where it is undefined.
Let f(x) = x^(1/3). Find the domain and range of f(x). Is the function one-to-one?