Question

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

Answer 1

To identify the graph of an even function, we need to remember that an even function meets the condition \( f(x) = f(-x) \) for all \( x \). This typically means that the graph is symmetric with respect to the y-axis.

From the descriptions provided:

1. The first image describes a parabola, which is typically even (for example, the graph of \( y = x^2 \) is symmetric around the y-axis).

2. The second and third images both involve lines passing through points. However, unless specified that the lines show symmetry (like a horizontal line or a vertical line that doesn't shift), they may not exhibit the symmetry required to be considered even.

Given that the first option describes a parabola, it is likely the graph of an even function.

Therefore, the correct choice for an even function is the graph of **the parabola** (first image).