Question

WhicWhich graph represents an even function?

On a coordinate plane, a hyperbola has a curve in quadrant 1 and a curve in quadrant 3. The curve in quadrant 1 has a vertex at (2, 2) and goes through points (1, 5) and (5, 1). The curve in quadrant 3 has a vertex at (negative 2, negative 2) and goes through points (negative 5, negative 1) and (negative 1, negative 5).
On a coordinate plane, a function has two curves. The first curve is asymptotic to x = negative 3, goes through (negative 2, 0), has a minimum of (negative 1.5, negative 1), goes through (negative 1, 0), and connects with the second curve at (0.5, 3). The second curve starts at (0.5, 3), goes through (2, 0), has a minimum of (2.5, negative 1), goes through (3, 0), and is asymptotic to x = 4.h graph represents an even function?

Answer 1

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Explanation:

Answer 2

The graph that represents an even function is the one described by the two-curve function.

An even function is a function that satisfies the condition f(x) = f(-x) for all x in its domain. In graphical terms, an even function has symmetry with respect to the y-axis.

Let's analyze the given information for each graph:

1. **Hyperbola in Quadrants 1 and 3:**

- Quadrant 1 vertex: (2, 2)

- Quadrant 3 vertex: (-2, -2)

- This hyperbola does not have symmetry about the y-axis, so it does not represent an even function.

2. **Two-Curve Function:**

- Asymptotic to x = -3

- First curve: Minimum at (-1.5, -1), goes through (-2, 0), (-1, 0)

- Second curve: Minimum at (2.5, -1), goes through (2, 0), (3, 0), asymptotic to x = 4

- This function has symmetry about the y-axis, so it represents an even function.

Therefore, the graph that represents an even function is the one described by the two-curve function.