Question

An open endpoint is plotted at left parenthesis 0 comma negative 5 right parenthesis and has a line extending upward and to the right. The line passes through left parenthesis 5 comma 0 right parenthesis and ends at left parenthesis 10 comma 5 right parenthesis. A closed endpoint is plotted at left parenthesis 0 comma 2 right parenthesis and has a line extending upward and to the left. The line passes through left parenthesis 3 comma 5 right parenthesis and ends at left parenthesis 5 comma 7.5 right parenthesis.

Which of the following piecewise functions matches the graph?

(1 point)

f(x)={−x−1 if x<1−x+2 if x≥1


f(x)={x+5 if x≤−22x+3 if x>−2


f(x)={2−x if x≤0x−5 if x>0


f(x)={−5 if x<0−x+1 if x≥0

Answer 1

The third option.

Reason: For x > 0, f(x) = x − 5 is the line through (0, −5) (open) and (5, 0), (10, 5). For x ≤ 0, f(x) = 2 − x gives f(0) = 2 (closed) and has slope −1 to the left. So f(x) = {2 − x if x ≤ 0; x − 5 if x > 0}.