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Suppose that the function f is defined f f(x)={(1-x² if x<1),(-2x+2 if x>=1):}

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Final answer:

The function f(x) is defined as 1 - x² for x < 1 and -2x + 2 for x ≥ 1. To draw the graph of f(x), evaluate f(x) for different values of x within the given interval and plot the points on a coordinate plane. To find P(2.5 < x < 7.5), calculate the area under the graph between x = 2.5 and x = 7.5.

Step-by-step explanation:

The function f(x) is defined as:

  • f(x) = 1 - x² if x < 1
  • f(x) = -2x + 2 if x ≥ 1

For the given function f(x) = , you are asked to draw the graph of f(x) for 0 ≤ x ≤ 8 and find P(2.5 < x < 7.5).

To draw the graph of f(x), you need to evaluate f(x) for different values of x within the given interval. For x < 1, f(x) = 1 - x². For x ≥ 1, f(x) = -2x + 2. Plot these points on a coordinate plane and join them to get the graph of f(x).

To find P(2.5 < x < 7.5), you need to find the area under the graph of f(x) between x = 2.5 and x = 7.5. This can be calculated by finding the area of the trapezoid formed by the graph of f(x) and the x-axis between x = 2.5 and x = 7.5.

User John Rayner
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