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
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