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I need the mathematical formula for this graphic

I need the mathematical formula for this graphic-example-1

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The piecewise function represented by the graph is

f(x) = 3/2x - 1 , for 0 ≤ x ≤ 2.

x = 2

f(x) = -2x + 5 , for 2 < x < 3.

f(x) = -1, for x > 3

Writing a piecewise function represented by the graph.

From the question, we have the following parameters that can be used in our computation:

The graph

The first linear piece goes through the points (0, -1) and (2, 2).

This can be represented by the equation of a line:

f(x) = mx - 1, where m is the slope.

Using the other point, we have

2m - 1 = 2

m = 3/2

So,

f(x) = 3/2x - 1 , for 0 ≤ x ≤ 2.

The second linear piece begins at an open dot at (2, 2) and ends at a closed dot at (2, 1).

This is a vertical line

So,

x = 2

The third linear piece goes through the points (2, 1) and (3, -1).

This can be represented by the equation of a line:

2m + c = 1

3m + c = -1

So, we have

m = -2

c = 1 - 2 * -2

c = 5

So,

f(x) = -2x + 5 , for 2 < x < 3.

Hence, the function is

f(x) = 3/2x - 1 , for 0 ≤ x ≤ 2.

x = 2

f(x) = -2x + 5 , for 2 < x < 3.

f(x) = -1, for x > 3

User Matt Gaunt
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