Subjects algebra

Stepwise Curve 8Fd430

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Stepwise Curve 8Fd430


1. The problem asks to create a graph similar to the described stepwise curve but different in values. 2. The original graph has three segments: an orange curve rising steeply from (1, -1) to (2, 1) then horizontal to (3, 1), a green curve rising steeply from (3, 1) to (4, 3) then horizontal to (5, 3), and blue horizontal lines from (0, -1) to (1, -1) and (4, 3) to (6, 3). 3. To create a similar graph, we keep the stepwise shape but change the points. 4. For example, let the first segment rise steeply from (2, 0) to (3, 2) then horizontal to (4, 2). 5. The second segment rises steeply from (4, 2) to (5, 4) then horizontal to (6, 4). 6. The horizontal lines can be from (1, 0) to (2, 0) and (5, 4) to (7, 4). 7. This preserves the stepwise shape but changes the coordinates. 8. The piecewise function for this graph is: $$ y=\begin{cases} 0 & 1 \leq x < 2 \\ 2(x-2) & 2 \leq x < 3 \\ 2 & 3 \leq x < 4 \\ 2(x-4)+2 & 4 \leq x < 5 \\ 4 & 5 \leq x < 7 \end{cases} $$ 9. This function rises steeply in the intervals [2,3) and [4,5), and is constant in [1,2), [3,4), and [5,7). 10. This matches the stepwise pattern requested but with different values.