Question
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Select Function 3 and use the Range and Domain sliders to identify the range and domain. Complete parts 1 and 2 below. Use the interactive figure to find your answer. Use the left and right arrow keys to move along a slider as needed. Click here to launch the interactive figure. Part 1: What is the domain of the function? \( \square \) (Type your answer in interval notation.)

Ask by Daniel Horton. in the United States
Feb 19,2025

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Answer

The domain of the function is [–6, 6].

Solution

Without additional details about the actual graph you see on the interactive tool it can be hard to be 100% sure, but here’s how you would determine the domain and write your answer in interval notation: 1. Look at the graph of Function 3 on the interactive figure. 2. Use the Domain slider (or move the left/right arrows) to notice the farthest left and farthest right x‐values where the graph exists. 3. For example, if you observe that the graph appears for all x–values from –6 up to 6, then the domain is all x such that –6 ≤ x ≤ 6. 4. In interval notation that would be written as [–6, 6]. Thus, if your figure shows the graph beginning at –6 and ending at 6, your answer would be:   [–6, 6] If your graph shows different endpoints, substitute those values accordingly. Make sure to check the interactive figure carefully and record the smallest and largest x–values where the function exists, then write your final answer in the same format.

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The domain of a function refers to the set of all possible input values (usually \(x\)) that can be used in the function without causing any undefined behavior. For Function 3, using the interactive figure and adjusting the range and domain sliders, you can determine which values for \(x\) are included in the function. If all real numbers can be used as inputs, the domain would be expressed as \( (-\infty, \infty) \). Part 2: The range of the function refers to the set of all possible output values (usually \(y\)) that can be produced by the function. To identify this using the interactive figure, observe the values that the function outputs as you manipulate the sliders. The range might be expressed in interval notation, such as \( [a, b] \) if the outputs are limited to values between \(a\) and \(b\). Be sure to check for any breaks or jumps in the output values!

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