Identify the graph of an even function from the following choices.(1 point)

Question

Responses

Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.

Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.

A curved line is graphed on a coordinate plane. The x-axis ranges from negative 5 to 5 in increments of 1. The y-axis ranges from negative 200 to 200 in increments of 100.
Image with alt text: A curved line is graphed on a coordinate plane. The x-axis ranges from negative 5 to 5 in increments of 1. The y-axis ranges from negative 200 to 200 in increments of 100.

A parabola is graphed on a coordinate plane. The x-axis ranges from negative 6 to 5 in increments of 1. They y-axis ranges from negative 2 to 16 in increments of 2.

Answer 1

To identify the graph of an even function, we look for a graph that is symmetric with respect to the y-axis. This means that if (x, y) is a point on the graph, then (-x, y) should also be a point on the graph.

Among the options provided, the following are potential candidates:

1. A line graph passing through five plotted points (it's unclear without more information whether it's symmetric).
2. Another line graph with the same description.
3. A curved line that could potentially represent an even function, but we need to see its symmetry.
4. A parabola, which is typically symmetric about the y-axis.

Given the typical characteristics of mathematical functions, the parabola is most likely to be the graph of an even function, as parabolas in standard form (y = ax² + bx + c) are symmetric about the y-axis when b = 0 (which gives a standard parabola opening up or down).

Thus, the graph that likely represents an even function is the parabola.