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Domain and Range Calculator
To find the domain and range of a function, you'll need to examine the possible inputs (domain) and outputs (range) of the function. A function is a relationship between inputs (x) and outputs (y) where each input produces only one output.
Here are the steps to find the domain and range of a function using a calculator:
1. Enter the function into your calculator.
2. Determine the possible values of x that can be input into the function. This is the domain of the function.
3. Evaluate the function for the values in the domain and determine the possible outputs (y). This is the range of the function.
For example, let's say you have the function f(x) = x^2 - 3x. To find the domain and range of this function, you would follow these steps:
1. Enter f(x) = x^2 - 3x into your calculator.
2. Determine the possible values of x that can be input into the function. In this case, there are no restrictions on the input values of x. Therefore, the domain is all real numbers or (-∞, +∞).
3. Evaluate the function for the values in the domain to determine the range. One way to do this is to use the vertex formula to find the minimum value of the function.
The vertex of the function is at (3/2, -9/4), which is the minimum value of the function. Since the function is a parabola that opens upwards, the range is all real numbers greater than or equal to -9/4, or [-9/4, +∞).
So the domain of f(x) = x^2 - 3x is (-∞, +∞), and the range is [-9/4, +∞).
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