The piecewise function is:
f(x) = x + 1 if x < 2
f(x) = -7x + 42 if x > 5
How to express the function graphed?
On the graph we can see a piecewise function (piecewise means that it has different equations defined for different intervals in the domain).
On the left side, we can see a linear equation that comes from negative infinity and ends at x = 2 with an open circle (so the domain does not contain that value).
That line passes through (-1, 0) and (0, 1), then the slope is:
a = (1 - 0)/(0 -(-1)) = 1
And the y-intercept is y = 1, then the equation of the line is:
y = x + 1
The other line starts at x = 5 (again, open circle) and keeps going, it passes through the points (5, 7) and (6, 0)
The slope is:
a = (0 - 7)/(6 -5) = -7
Then the line is something like:
y = -7*x + b
To find b, we use the point (6, 0)
0 = -7*6 + b
7*6 = 42 = b
Then this line is:
y = -7x + 42
Concluding, the piecewise function is:
f(x) = x + 1 if x < 2
f(x) = -7x + 42 if x > 5
If you want to learn more about piecewise functions:
https://brainly.com/question/3628123
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