Note that the domain and range are always written from smaller to larger values, or from left to right for domain, and from the bottom of the graph to the top of the graph for range. We can observe that the graph extends horizontally from −5 to the right without bound, so the domain is \(\left\). This piecewise function represents the cost of f(x) for x number of guests.\): Graph of a polynomial that shows the x-axis is the domain and the y-axis is the range We can now summarize this into a piecewise function: For this interval, f(x) will always be equal to 60. Now, for a table with 6 or more people, we can express the interval as x ≥ 6.Since it would cost each guest $6, the total for x guests is 6x. The range of a function is all the possible values of the dependent variable y. For a table of 1 to 5 guests, we can express that as 1 ≤ x ≤ 5 in terms of x. The domain and range of a function is all the possible values of the independent variable, x, for which y is defined.Let’s go ahead and break down the problem and find the expression of f(x) for each interval: Write a function that relates the number of people, x, and the cost of attending the event, f(x). They also offer a fixed fee of $50 for a table with 6 or more people. They charge $6 per person for a table of 1 to 5 guests. Spoken word poetry is being held at the nearby cafe. Since the graph only covers the values of y above the x-axis, the range of the function is [0, ∞ ) in interval notation. Since all values of x extend in both directions, the domain would be all real numbers or (-∞, ∞). Let’s go ahead and simplify this graph now so that we can analyze it for its domain and range. The image above breaks down the three components of the piecewise function. Using this information, we can now graph f(x). When x ≥ 2, f(x) is a function and will pass through (2, 1) and (6,3).Make sure to leave (0,5) and (2,5) unfilled since they are not part of the solution. ![]()
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