Question

The graph of a function is shown.

On a coordinate plane, a function has 2 connecting line. The first line goes from (negative 5, negative 2) to (0, 3). The second line starts at (0, 3) and continues horizontally at y = 3.
Which function is represented by the graph?

f(x) = StartLayout enlarged left-brace 1st Row 1st column x minus 3, 2nd column x less-than 0 2nd Row 1st column 3, 2nd column x greater-than-or-equal-to 0 EndLayout
f(x) = StartLayout enlarged left-brace 1st Row 1st column x + 3, 2nd column x less-than 0 2nd Row 1st column 3, 2nd column x greater-than-or-equal-to 0 EndLayout
f(x) = StartLayout enlarged left-brace 1st Row 1st column negative x + 3, 2nd column x less-than-or-equal-to 0 2nd Row 1st column 3, 2nd column x greater-than 0 EndLayout
f(x) = StartLayout enlarged left-brace 1st Row 1st column negative x minus 3, 2nd column x less-than-or-equal-to 0 2nd Row 1st column 3, 2nd column x greater-than 0 EndLayout

Answer 1

Answer: f(x) = { x + 3, x < 0; 3, x ≥ 0 }.

Reason: The line through (-5,-2) and (0,3) has slope (3 - (-2))/(0 - (-5)) = 5/5 = 1, so its equation is y = x + 3 for x < 0. For x ≥ 0 the graph is the horizontal line y = 3.