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Which 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.

On a coordinate plane, a parabola opens down. It goes through (negative 2, 0), has a vertex at (0, 4), and goes through (2, 0).

On a coordinate plane, a straight line has a negative slope. It goes through (negative 2, 4), crosses the y-axis at (0, 2), and crosses the x-axis at (2, 0).

Respuesta :

Answer:

one to one function

Step-by-step explanation:

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Using the concept of even function, it is found that the graph that represents an even function is the third option, given by:

On a coordinate plane, a parabola opens down. It goes through (-2, 0), has a vertex at (0, 4), and goes through (2, 0).

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  • For an even function, [tex]\mathbf{f(x) = f(-x)}[/tex] for all values of x.

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  • For the first option, [tex]f(1) = 5[/tex], and [tex]f(-1) = -5[/tex], thus [tex]\mathbf{f(x) \neq f(-x)}[/tex], and the function is not even.
  • For the second option, there are asymptotes, thus, it is not even.
  • For the third option, from the information given, [tex]\mathbf{f(-2) = f(2)} = 0[/tex], we suppose this extends for all values of x, thus, it is even, and this is the correct option.
  • For the fourth option, [tex]f(-2) = 4[/tex] and [tex]f(2) = 0[/tex], thus [tex]\mathbf{f(-x) \neq f(x)}[/tex], and the function is not even.

A similar problem is given at https://brainly.com/question/16711376