Math Problem Solver

The domain of the piecewise function is ​(minusinfinity​,infinity​).

a. Graph the function.

b. Use your graph to determine the​ function's range.

​f(x)equalsleft brace Start 2 By 3 Matrix 1st Row 1st Column x plus 2 2nd Column if 3rd Column x less than minus 1 2nd Row 1st Column x minus 2 2nd Column if 3rd Column x greater than or equals minus 1 EndMatrix

Question content area bottom

Part 1

a. Choose the correct graph below.

A.

-10

10

-10

10

x

y

A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 2 and a vertical y-axis labeled from negative 10 to 10 in increments of 2. A graph has two branches. The first branch is a ray that falls from right to left, starting at a solid circle at (negative 1, 3) and passing through the points (negative 2, 2) and (negative 3, 1). The second branch is ray that rises from left to right, starting at an open circle at (negative 1, negative 1) and passing through the points (0, 0) and (1, 1).

B.

-10

10

-10

10

x

y

A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 2 and a vertical y-axis labeled from negative 10 to 10 in increments of 2. A graph has two branches. The first branch is a ray that rises from right to left, starting at a solid circle at (negative 1, negative 1) and passing through the points (negative 9, 7) and (negative 10, 8). The second branch is ray that falls from left to right, starting at an open circle at (negative 1, 3) and passing through the points (9, negative 7) and (10, negative 8).

C.

-10

10

-10

10

x

y

A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 2 and a vertical y-axis labeled from negative 10 to 10 in increments of 2. A graph has two branches. The first branch is a ray that rises from right to left, starting at an open circle at (negative 1, negative 3) and passing through the points (negative 2, negative 2) and (negative 3, negative 1). The second branch is ray that falls from left to right, starting at a solid circle at (negative 1, 1) and passing through the points (0, 0) and (1, negative 1).

D.

-10

10

-10

10

x

y

A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 2 and a vertical y-axis labeled from negative 10 to 10 in increments of 2. A graph has two branches. The first branch is a ray that falls from right to left, starting at an open circle (negative 1, 1) and passing through the points (negative 9, negative 7) and (negative 10, negative 8). The second branch is ray that rises from left to right, starting at a solid circle at (negative 1, negative 3) and passing through the points (9, 7) and (10, 8).

Your answer is correct.

Part 2

b. What is the range of the entire piecewise​ function? Select the correct choice below​ and, if​ necessary, fill in the answer​ box(es) to complete your choice.

A.

The range does not have any isolated values. It can be described by

enter your response here. ​(Type your answer in interval​ notation.)

B.

The range has at least one isolated value. It can be described as the union of the​ interval(s)

enter your response here and the set StartSet nothing EndSet

. ​(Use a comma to separate answers as​ needed.)

C.

The range consists exclusively of one or more isolated values. It can be described as StartSet nothing EndSet

. ​(Use a comma to separate answers as​ needed.)