Answer:
Step-by-step explanation:
These are graphs of piecewise functions.
Each part is a graph of the linear function.
The slope-intercept form of an equation of a line:
<em>m</em><em> - slope</em>
<em>b</em><em> - y-intercept → (0, b)</em>
The formula of a slope:
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<h2>a)</h2>Part 1:
Points (0, 2) → <em>b = 2</em>, and (2, 0).
Calculate the slope:
Put the value of <em>m</em> and <em>b</em> to the equation of a line:
Part 2:
Points (2, 1) and (5, 0).
Calculate the slope:
Put the value of the slope and the coordinates of the point (5, 0) to the equation of a line:
<em>add 5/3 to both sides</em>
Therefore we have:
The domain of the function is (0, 2] and (2, 5].
Formula of the piecewise function:
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<h2>b)</h2>We solve the same as in a) in Part 1
Part 1:
(-1, 0), (0, -3) → <em>b = -3</em>
Part 2:
(0, 3) → <em>b = 3</em>, (2, -1)
Domain: (-1, 0] and (0, 2].