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

Answer 1

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**.