Domain And Range Questions And Answers Pdf Class 11

Introduction to Domain and Range

In mathematics, domain and range are important concepts that are used to describe the behavior of a function. The domain of a function is the set of all possible input values for which the function is defined. The range of a function is the set of all possible output values that the function can produce.

When we look at the behavior of a function, we need to know its domain and range. These values can help us understand how the function behaves, and what it can do. For example, if the domain of a function is restricted to positive numbers, we can be sure that the function will never produce a negative output.

Domain and Range for Quadratic Functions

The domain and range of a quadratic function can be determined by looking at its graph. A quadratic function is a function of the form f(x) = ax2 + bx + c, where a, b, and c are constants.

The domain of a quadratic function is all real numbers. This is because, for any value of x, we can always find a corresponding value of y that satisfies the equation. However, the range of a quadratic function is determined by the coefficient a. If a > 0, the range will be all positive numbers, and if a < 0, the range will be all negative numbers.

Domain and Range for Exponential Functions

Exponential functions are functions of the form f(x) = a•bx, where a and b are constants. The domain of an exponential function is all real numbers, because we can always plug in any value of x and get a valid output.

The range of an exponential function, however, depends on the value of b. If 0 < b < 1, the range will be all positive numbers, but it will approach zero as x goes to infinity. If b > 1, the range will be all positive numbers, and it will increase without bound as x goes to infinity.

Domain and Range for Logarithmic Functions

Logarithmic functions are functions of the form f(x) = logb(x), where b is a positive constant. The domain of a logarithmic function is all positive real numbers, because we can only take the logarithm of a positive number.

The range of a logarithmic function depends on the base of the logarithm. If the base is greater than 1, the range will be all real numbers. If the base is between 0 and 1, the range will be all negative numbers. If the base is 1, the function is undefined.

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Sample Domain and Range Problems

Now that we understand what domain and range are and how they behave for different types of functions, let's look at some sample problems.

1. Find the domain and range of the function f(x) = 1/x.

Solution: The domain of this function is all real numbers except 0, because we cannot divide by zero. The range is all real numbers except 0, because the function will approach zero as x approaches infinity or negative infinity.

2. Find the domain and range of the function f(x) = sin(x).

Solution: The domain of this function is all real numbers, because sine is defined for all values of x. The range is between -1 and 1, because the value of sine can never be greater than 1 or less than -1.

Conclusion

In conclusion, understanding domain and range is essential for solving mathematical problems related to functions. By knowing what domain and range are and how they behave for different types of functions, we can easily determine the behavior of a function and solve complex problems using simple techniques.

Remember, the domain of a function is the set of all possible input values for which the function is defined, while the range is the set of all possible output values that the function can produce. With this knowledge, you can solve any domain and range problem thrown your way!