Question

Which is the graph of the piecewise function f(x)?

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

On a coordinate plane, a piecewise function has 2 connecting lines. The first line goes from (4, 5) down to (0, 1). The second line goes from (0, 1) up through (4, 5).

On a coordinate plane, a piecewise function has 2 connecting lines. The first line goes from (4, 5) down to (1, 0). The second line goes from (1, 0) up through (4, 3).

On a coordinate plane, a piecewise function has 2 connecting lines. The first line goes from (negative 5, negative 4) up to (0, 1). The second line goes from (0, 1) down through (4, negative 3).

On a coordinate plane, a piecewise function has 2 connecting lines. The first line goes from (negative 4, negative 5) up to (1, 0). The second line goes from (1, 0) down through (4, negative 3).

Answer 1

The first graph.

Reason: f(0)=1. For x≤0, f(x) = -x+1 (slope −1) gives points like (−4,5) → (0,1). For x>0, f(x)=x+1 (slope +1) gives points like (0,1) → (4,5). So the V-shaped graph with a minimum at (0,1) and points (−4,5) and (4,5) matches the first option.