Question

The piecewise function f(x) has opposite expressions.

f(x) = StartLayout Enlarged left-brace 1st Row 1st column 2 x minus 1, 2nd column x less-than 0 2nd Row 1st column 0, 2nd column x = 0 3rd Row 1st column negative 2 x + 1, 2nd column x greater-than 0

Which is the graph of f(x)?

On a coordinate plane, a piecewise function has 2 lines. The first line goes through (negative 3, 4) and goes down to a closed circle at (negative 1, 0). The second line has a closed circle at (1, 0) and goes up through (3, 4).

On a coordinate plane, a piecewise function has 2 lines. The first line goes up through (negative 3, negative 4) to a closed circle at (0, 2). The second line has a closed circle at (0, 2) and goes down through (3, negative 4).

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

On a coordinate plane, a piecewise function has 2 lines. The first line goes down through (negative 1, 3) to a closed circle at (0, 1). The second line has a closed circle at (0, negative 1) and goes up through (2, 3).

Answer 1

y = 2x − 1 for x < 0 and y = −2x + 1 for x > 0.

Left branch: y = 2x − 1 passes through (−2, −5) and approaches (0, −1) as x → 0− (open at (0, −1)).
Right branch: y = −2x + 1 passes through (2, −3) and approaches (0, 1) as x → 0+ (open at (0, 1)).
f(0) = 0 gives a filled dot at (0,0).

The description that matches those line points (left through (−2, −5) to (0, −1), right through (2, −3) from (0,1)) is the third graph.