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. 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 even. The function is odd. The function is odd. The function is neither even nor odd. The function is neither even nor odd. The function is both even and odd.
The correct statement is: The function is neither even nor odd.
Based on the description of the graph, the wave starts oscillating on the negative x-axis, passes through the origin, and then continues to oscillate on the positive x-axis. The height of each wave increases the closer the function gets to the origin. Since the wave is symmetrical around the point (0,0), this means that for every x-value, there is a corresponding -x value that gives the same y-value. Therefore, the function is an example of an even function.
So, the statement "The function is even" is true.
To determine if the function is even or odd based on the given graph, we need to understand the definitions of these terms.
1. Even Function: A function is even if it is symmetrical about the y-axis. In other words, when you reflect the graph across the y-axis, it remains unchanged.
2. Odd Function: A function is odd if it is 180 degrees rotational symmetrical about the origin. In other words, when you rotate the graph by 180 degrees (half a turn) around the origin, it remains unchanged.
Looking at the description of the graph, it starts oscillating on the negative x-axis, passes through the origin, and continues to oscillate on the positive x-axis. The height of the wave increases as it gets closer to the origin.
This description indicates that the graph is symmetrical around the point (0,0), which means it is symmetrical about the y-axis. Therefore, the correct statement about the function is:
The function is even.
Explanation: The symmetry around the y-axis indicates that when the graph is reflected across the y-axis, it remains unchanged. This aligns with the definition of an even function.