Respuesta :
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