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)={−5 if x<0−x+1 if x≥0

f(x)={2−x if x≤0x−5 if x>0

f(x)={x+5 if x≤−22x+3 if x>−2

f(x)={−x−1 if x<1−x+2 if x≥1

Answer 1

f(x) = { 2 − x for x ≤ 0; x − 5 for x > 0 }

Reason: For x ≤ 0 the line y = 2 − x has value 2 at x = 0 (closed dot at (0,2)) and slope −1 (goes up to the left). For x > 0 the line y = x − 5 passes through (5,0) and is open at (0,−5), matching the right-hand segment.