Question

Which of the following is the graph of the piecewise function h of x is defined as negative x squared plus 2 for x is less than or equal to negative 2, or one half times x for negative 2 is less than x is less than 2, or x squared minus 2 for x greater than or equal to 2.?

Answer 1

The piecewise function h(x) is defined as follows:

For x ≤ -2: h(x) = -x^2 + 2

For -2 < x < 2: h(x) = (1/2) * x

For x ≥ 2: h(x) = x^2 - 2

To graph this piecewise function, you would draw separate portions of the graph for each segment of the function and connect them.

For x ≤ -2, the graph is a downward-opening parabola with its vertex at (-2, 2).

For -2 < x < 2, the graph is a straight line with a slope of 1/2 and passing through the point (0, 0).

For x ≥ 2, the graph is an upward-opening parabola with its vertex at (2, -2).

Explanation: