Question

A function, h(x), is defined as shown.

h(x) = StartLayout Enlarged left-brace 1st row 1st column one-fourth x minus 4, 2nd column x less-than-or-equal-to 0 2nd row 1st column one-third x minus 3, 2nd column 0 less-than x less-than-or-equal-to 3, 3rd row 1st column one-half x minus 2, 2nd column x greater-than-or-equal-to 4

Which graph represents h(x)?

On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 4, 0) and goes up to a closed circle at (0, 1). The second line starts at (0, negative 3) and goes up to a closed circle at (3, negative 2). The third line has a closed circle at (4, negative 2) and goes up to (6, negative 1).

On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 4, negative 5) and goes up to a closed circle at (0, negative 4). The second line starts at (0, negative 3) and goes up to a closed circle at (3, negative 2). The third line has a closed circle at (4, 0) and goes up to (6, 1).

On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 4, 3) and goes up to a closed circle at (0, 4). The second line starts at (0, 3) and goes up to a closed circle at (3, 4). The third line has a closed circle at (4, 4) and goes up to (6, 5).

On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 4, 0) and goes up to a closed circle at (0, 1). The second line starts at (0, negative 1) and goes up to a closed circle at (3, 0). The third line has a closed circle at (4, negative 2) and goes up to (6, negative 1).

Mark this and return

Answer 1

The second graph.

Reason: h(-4)=1/4(-4)-4=-5 so first segment is (-4,-5) to (0,-4) (closed at 0). For 0<x≤3, h(x)=1/3 x-3 so it runs from (0,-3) (open) to (3,-2) (closed). For x≥4, h(x)=1/2 x-2 so (4,0) (closed) to (6,1). These match the second option.