A graph of a piecewise defined function is shown on the coordinate plane.A graph of a piecewise defined function is shown on the coordinate plane. The x axis goes from negative 5 to 10 and the y axis goes from negative 10 to 5. The function starts with an arrow pointing down to the left and a line goes up to the right to the point left-parenthesis negative 2 comma negative 2 right-parenthesis. The function then moves horizontally to the right to the point left-parenthesis 2 comma negative 2 right-parenthesis. From here, the function travels up to the right to the point left-parenthesis 4 comma 0 right-parenthesis. The last piece of the function starts here and curves down and to the right passing through the point left-parenthesis 8 comma negative 2 right-parenthesis and ends with an arrow pointing down and to the right.

Question

A graph of a piecewise defined function is shown on the coordinate plane.A graph of a piecewise defined function is shown on the coordinate plane. The x axis goes from negative 5 to 10 and the y axis goes from negative 10 to 5. The function starts with an arrow pointing down to the left and a line goes up to the right to the  point left-parenthesis negative 2 comma negative 2 right-parenthesis. The function then moves horizontally to the right to the point left-parenthesis 2 comma negative 2 right-parenthesis. From here, the function travels up to the right  to the point left-parenthesis 4 comma 0 right-parenthesis. The last piece of the function starts here and curves down and to the right passing through the point left-parenthesis 8 comma negative 2 right-parenthesis and ends with an arrow pointing down and to the right.
Question
Use the graph to answer the question.
Identify the x-values for which f left-parenthesis x right-parenthesis greater than negative 2.
(1 point)
Responses

left-parenthesis x vertical line 2 less-than-or-equal-to x less-than-or-equal-to 8 right-parenthesis
Image with alt text: left-parenthesis x vertical line 2 less-than-or-equal-to x less-than-or-equal-to 8 right-parenthesis

left-parenthesis x vertical line negative 2 less-than-or-equal-to x less-than-or-equal-to 2 right-parenthesis
Image with alt text: left-parenthesis x vertical line negative 2 less-than-or-equal-to x less-than-or-equal-to 2 right-parenthesis

left-parenthesis x vertical line negative 2 less than x less than 8 right-parenthesis
Image with alt text: left-parenthesis x vertical line negative 2 less than x less than 8 right-parenthesis

left-parenthesis x vertical line 2 less than x less than 8 right-parenthesis

GPT-4o mini · Answer

To determine the x-values for which $ f(x) > -2 $ based on the graph description, observe the following: 1. From $ x = -2 $ to $ x = 2 $, the function is horizontal at $ y = -2 $. At these endpoints, $ f(x) $ is equal to -2, not greater than -2. 2. From $ x = 2 $ to $ x = 4 $, the function goes upwards and thus $ f(x) $ is greater than -2 in this interval. 3. From $ x = 4 $ to $ x = 8 $, the function curves downwards, starting from $ y = 0 $ and passing through $ (8, -2) $. For $ x $ values in this range, $ f(x) > -2$ until it reaches $ (8, -2) $. Thus, the intervals where $ f(x) > -2 $ are: - From $ x = 2 $ to $ x = 8 $. Therefore, the correct interval is: $$ \text{(} x \mid 2 < x < 8 \text{)} $$ So, the response is: **left-parenthesis x vertical line 2 less than x less than 8 right-parenthesis**.