Math Problem Statement

Question content area top Part 1 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)equalsStartSet Start 3 By 3 Matrix 1st Row 1st Column 0 2nd Column if 3rd Column x less than minus 3 2nd Row 1st Column negative 2 x 2nd Column if 3rd Column negative 3 less than or equals x less than 0 3rd Row 1st Column x squared 2nd Column if 3rd Column x greater than or equals 0 EndMatrix

Question content area bottom Part 1 a. Choose the correct graph below. A. -10 10 -20 20 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 20 to 20 in increments of 4. A graph has three branches. The first branch is a horizontal ray that extends to the left from an open circle at (negative 3, 0). The second branch is a line segment that falls from a solid circle at (negative 3, 6) to the point (0, 0). The third branch is a curve that falls from left to right at an increasing rate, starting at the point (0, 0) and passing through the points (1, negative 1) and (2, negative 4). B. -10 10 -20 20 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 20 to 20 in increments of 4. A graph has three branches. The first branch is a horizontal ray that extends to the left from an open circle at (negative 3, 0). The second branch is a line segment that falls from a solid circle at (negative 3, 6) to the point (0, 0). The third branch is a curve that rises from left to right at an increasing rate, starting at the point (0, 0) and passing through the points (1, 1) and (2, 4). C. -10 10 -20 20 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 20 to 20 in increments of 4. A graph has three branches. The first branch is a horizontal ray that extends to the left from an open circle at (negative 3, 0). The second branch is a line segment that rises from a solid circle at (negative 3, negative 6) to the point (0, 0). The third branch is a curve that falls from left to right at an increasing rate, starting at the point (0, 0) and passing through the points (1, negative 1) and (2, negative 4). D. -10 10 -20 20 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 20 to 20 in increments of 4. A graph has three branches. The first branch is a curve that falls from left to right at an increasing rate passing through the points (negative 2, 4) and (negative 1, 1) to the point (0, 0). The second branch is a line segment that rises from the point (0, 0) to a solid circle at (3, 6). The third branch is a horizontal ray that extends to the right from an open circle at (3, 0). 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   

Solution

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Math Problem Analysis

Mathematical Concepts

Piecewise Functions
Graphing Functions
Quadratic Functions
Linear Functions
Interval Notation

Formulas

f(x) = 0 if x < -3
f(x) = -2x if -3 ≤ x < 0
f(x) = x^2 if x ≥ 0

Theorems

Range of a function
Properties of piecewise functions
Quadratic function behavior
Continuity and discontinuity at boundary points

Suitable Grade Level

Grades 10-12