I can provide some examples of problems you might find in a domain and range worksheet.
Example 1:
Find the domain and range of the function f(x) = 2x + 1.
Solution:
The domain of this function is all real numbers because there are no restrictions on the input x. The range of the function is all real numbers because every real number can be obtained as a possible output value by selecting an appropriate value of x.
Domain: All real numbers
Range: All real numbers
Example 2:
Find the domain and range of the function g(x) = √(4 - x^2).
Solution:
To find the domain of this function, we need to determine the set of all possible input values that will produce a real output value. Since the square root of a negative number is not a real number, the expression 4 - x^2 must be non-negative. This leads to the inequality -2 ≤ x ≤ 2. Therefore, the domain of the function is the closed interval [-2, 2]. To find the range, we notice that the expression √(4 - x^2) is always non-negative, which means the range of the function is the closed interval [0, 2].
Domain: [-2, 2]
Range: [0, 2]
Example 3:
Find the domain and range of the function h(x) = 1/(x^2 - 4).
Solution:
To find the domain of this function, we need to determine the set of all possible input values that will produce a real output value. Since the expression x^2 - 4 appears in the denominator, the function is not defined when x = 2 or x = -2 (division by zero is undefined). Therefore, the domain of the function is the set of all real numbers except 2 and -2. To find the range, we notice that the expression 1/(x^2 - 4) is always negative when x is between -2 and 2, and it is always positive when x is less than -2 or greater than 2. Therefore, the range of the function is the set of all negative numbers and all positive numbers.
Domain: All real numbers except 2 and -2
Range: All negative numbers and all positive numbers
These are just a few examples of the types of problems you might see on a domain and range worksheet. The specific functions and methods used to find the domain and range can vary, but the general idea is to determine the set of all possible input values and output values for the given function.
