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

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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.
Image with alt text: 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.

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.

1 answer

To identify the graph of an even function, we need to look for symmetry. An even function is symmetric with respect to the y-axis, meaning that for every point \((x, y)\) on the graph, there is also a point \((-x, y)\).

  1. The first option describes a line with five plotted points, but without seeing the specifics of the points, we cannot determine its symmetry.

  2. The second option mentions a curved line, which might or might not be symmetric, but we need more specifics to analyze.

  3. The third option describes a parabola, which is always symmetric about the y-axis if it opens upwards or downwards. Therefore, it is likely that this is the even function you are looking for.

  4. The final option again describes a line with five points, similar to the first option, and we cannot determine its symmetry without more details.

Given this analysis, the graph of the parabola is the graph of an even function.