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TRAN Unit 5A Sample Work: Domain and Range of Functions
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To find the domain and range of a function, you need to understand what these terms mean.
The domain of a function is the set of all possible input values, or the values for which the function is defined. In other words, it's the set of x-values that you can plug into the function to get an output. To find the domain, you need to consider any restrictions or limitations on the input values.
The range of a function is the set of all possible output values, or the values that the function can take on. In other words, it's the set of y-values that the function can produce. To find the range, you need to determine the possible outputs of the function for the given domain.
Here's a step-by-step process to find the domain and range of a function:
1. Start by identifying the function. It could be given in different forms such as an equation, a table, or a graph.
2. For the domain, consider any restrictions on the input values. Look for things like division by zero or taking the square root of a negative number. These situations would create undefined values.
3. If there are no explicit restrictions, then the domain is usually all real numbers unless otherwise specified.
4. For the range, examine the output values of the function. Look for patterns in the set of y-values for the given x-values.
5. If the function is defined by an equation, try to algebraically manipulate it to solve for the dependent variable (usually y). This might involve isolating y or rewriting the equation in terms of y.
6. If the function is represented by a table or a graph, try to observe the pattern or behavior of the y-values.
7. If you encounter vertical lines that cross the graph at multiple points, it indicates that the function has multiple y-values for a particular x-value. In this case, the range would be a set, and you need to write it as such.
It's important to note that finding the domain and range of a function can be more straightforward for certain types of functions, while it can be more complex for others. It often requires a combination of logical thinking, algebraic manipulation, and graphical analysis.