Based on the image you sent, which shows four graphs labeled A, B, C, and D, the graph of x^2 < 16 is: C. The graph with two open circles at -4 and 4, and a curved line passing through both points but not touching the x-axis.
Here's why:
The inequality x^2 < 16 describes all real numbers whose squares are less than 16.
Squaring any real number will result in a non-negative value (0 or greater).
Therefore, the graph of x^2 < 16 cannot touch the x-axis (which represents 0).
Let's analyze the other graphs:
Graph A: This graph shows a parabola that intersects the x-axis at -4 and 4. However, it also includes the part of the curve below the x-axis, which doesn't satisfy the inequality x^2 < 16.
Graph B: This graph shows a parabola that goes below the x-axis between -4 and 4. Since the inequality specifies values less than 16, not including negative values, this graph is also not accurate.
Graph D: This graph shows two horizontal lines at -4 and 4. While these numbers satisfy the inequality, they represent only two specific points, not all real numbers less than 16 as required.
Therefore, only graph C accurately represents the inequality x^2 < 16 by showing all real numbers whose squares are less than 16 (between -4 and 4) without including any values on the x-axis or below it.