First, sketch a graph of the following piecewise function.𝑓(𝑥)=⎧⎩⎨⎪⎪−101𝑥<00≤𝑥<11≤𝑥Determine whether there are any points of discontinuity and write the 𝑥-values in curly braces, e.g. {10,12}. Enter empty braces {} if there are no points of discontinuity.
Question
First, sketch a graph of the following piecewise function.𝑓(𝑥)=⎧⎩⎨⎪⎪−101𝑥<00≤𝑥<11≤𝑥Determine whether there are any points of discontinuity and write the 𝑥-values in curly braces, e.g. {10,12}. Enter empty braces {} if there are no points of discontinuity.
Solution
To sketch the graph of the piecewise function, you would need to break it down into its three parts:
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For x < 0, f(x) = -1. This is a horizontal line at y = -1 for all x-values less than 0.
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For 0 ≤ x < 1, f(x) = 0. This is a horizontal line at y = 0 for all x-values between 0 and 1, including 0 but not including 1.
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For 1 ≤ x, f(x) = 1. This is a horizontal line at y = 1 for all x-values greater than or equal to 1.
The points of discontinuity are the x-values where the function jumps from one value to another. In this case, the function jumps at x = 0 and x = 1. Therefore, the points of discontinuity are {0, 1}.
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