Monomial Functions — Quiz

Question 3 • Algebra 2 with Probability

Which is the graph of an odd 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, a curved graph is drawn. It passes through (negative 3 comma negative 6) and (negative 2 comma 0), curves to the right, crosses the y axis at (0 comma 2) and continues to curve to the right. It then passes through (2 comma 5).

Image with description On a coordinate plane with x and y axes listed from negative 8 to 8 with an increment of 1, a parabola is drawn. It opens upwards and has its vertex at the origin (0 comma 0). It passes through (negative 4 point 5 comma 6), (negative 3 comma 3), (3 comma 3) and (4 point 5 comma 6).

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

Image with description On a coordinate plane with x and y axes listed from negative 8 to 8 with an increment of 1, a curved graph is drawn. It passes through (1 comma negative 7), curves to the right, crosses the x axis at (4 comma 0) and continues to curve to the right. It then passes through (7 comma 7).

Explanation

An odd monomial has the form f(x) = a xⁿ, where n is an odd positive integer. Its graph passes through the origin and has symmetry about the origin. Choice C passes through (0, 0), and its points (−1, 2) and (1, −2) show that it is the line f(x) = −2x, an odd monomial. The other graphs either do not pass through the origin or are symmetric about the y-axis.

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