Monomial Functions — Quiz

Question 5 • Algebra 2 with Probability

Which is the graph of an even monomial function?

Answer

Image with description On a coordinate plane with x and y axes listed from negative 8 to 8 with an increment of 1, there is a curved graph. It passes through (negative 2 comma negative 8), bends to the right and passes through the origin and curves to the left and passes through (2 comma 8).

Image with description On a coordinate plane with x and y axes listed from negative 8 to 8 with an increment of 1, there is a parabola that opens upwards and has its vertex at (0 comma negative 4). It passes through (negative 2 comma 4) and (2 comma 4).

Image with description On a coordinate plane with x and y axes listed from negative 8 to 8 with an increment of 1, there is a curved graph in the shape of W. It passes through (negative 2 point 5 comma 8), crosses the x axis at (negative 2 comma 0) and bends three times at (negative 1 point 5 comma negative 2), (0,0) and (1 point 5 comma negative 2). It then crosses the x axis at (2 comma 0) and passes through the point (2 point 5 comma 8).

Image with description On a coordinate plane with x and y axes listed from negative 8 to 8 with an increment of 1, there is a parabola that opens upwards and passes through the origin. It passes through (negative 2 comma 6) and (2 comma 6).

Explanation

An even monomial has the form f(x) = a xⁿ, where n is even, so its graph is symmetric about the y-axis and passes through the origin. Choice D is an upward-opening parabola through the origin, with matching points at (−2, 6) and (2, 6), consistent with a monomial such as f(x) = 1.5x². Choice B is shifted downward, so it is not a monomial.

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