Fresnel integrals are functions that describe how light bends, and they are often used in the design of highways, railroads, and roller coasters. The graph shown is an approximation of the Fresnel integral. Use the graph to determine which of the following statements about the function is true.
A function is graphed on a coordinate plane.A function is graphed on a coordinate plane. The x-axis goes from negative 5 to 5 and the y-axis goes from negative 1 to 1. The graph is a wave that starts oscillating on the negative x-axis, passes through the origin, then continues to oscillate on the positive x-axis. The height of each wave increases the closer the function gets to the origin. The wave is symmetrical around the point left parenthesis 0 comma 0 right parenthesis.
(1 point)
Responses
The function is even.
The function is odd.
The function is neither even nor odd.
The function is both even and odd.
The function is odd.
Based on the given description of the graph, we can determine that the function is symmetrical around the point (0,0). This indicates that the function is an even function. Therefore, the correct statement is:
The function is even.
To determine whether the function is even, odd, both even and odd, or neither even nor odd, we need to understand the properties of these types of functions.
An even function is symmetric with respect to the y-axis. This means that for any x-value, the corresponding y-value is the same as the y-value for its opposite x-value. In other words, if (x, y) is on the graph, then (-x, y) is also on the graph.
An odd function, on the other hand, is symmetric with respect to the origin. This means that for any x-value, the corresponding y-value is the negative of the y-value for its opposite x-value. In other words, if (x, y) is on the graph, then (-x, -y) is also on the graph.
Looking at the given graph description, we can see that the wave is symmetrical around the origin. This implies that for any x-value, the corresponding y-value has the same magnitude but opposite sign.
Therefore, the function is odd since it is symmetric with respect to the origin.
Hence, the correct statement is:
The function is odd.