Functions  Domain and Range  Infinity Learn  (GMAT/GRE/CAT/Bank PO/SSC CGL)  Summary and Q&A
TL;DR
Domain is the set of all possible input values for a function, while range is the set of all possible output values.
Key Insights
 🧡 Domain and range are crucial concepts in understanding functions.
 😫 The domain refers to the set of all possible input values for a function, while the range refers to the set of all possible output values.
 0️⃣ The domain can be any value except for certain constraints, such as zero in the denominator for a fraction.
 🧡 The range can be determined based on the nature of the function, such as the nonnegativity constraint for even roots.
 🧡 Understanding the domain and range of a function is important in analyzing its behavior and graphing it accurately.
 🧡 The domain and range can vary depending on the specific function being analyzed.
 🧡 The domain and range of a function can be determined by examining the constraints and properties of the function's equation.
Questions & Answers
Q: What is the domain of a function?
The domain of a function is the set of all possible input values that can be used in the function. It represents the values that can be substituted for the independent variable.
Q: What is the range of a function?
The range of a function is the set of all possible output values that can be obtained from the function. It represents the values that can be obtained as a result of substituting the input values into the function.
Q: How can we remember that the domain is all possible input values and the range is all possible output values?
One way to remember this is to associate D (domain) with X (input) and R (range) with Y (output). Since X comes before Y and D comes before R, we can remember that domain is X and the range is Y.
Q: What are the common constraints in determining the domain of a function?
One common constraint is that the denominator of a fraction in the function cannot be zero, as it would result in an undefined function. Another constraint is for functions with even roots, where the number under the root has to be nonnegative.
Summary & Key Takeaways

Domain is the set of all possible input values for a function, while range is the set of all possible output values.

The domain for a function is all values that go into the function, while the range is the values that come out.

For a function like y = f(x), the domain is the set of all possible values x can take, and the range is the set of all possible values for y.