Transformations of Functions — Quiz

Question 2 • Mathematics III

Which graph is an example of a cubic function?

Answer

Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. A straight line with a positive extending infinitely in both positive x and y directions.

Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. There is a curve that approaches x equals negative 2 in quadrant 3, increases to a point of inflection at (0, 1), and then increases again and approaches x equals 2.

Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. The V-shaped graph opening downwards has a vertex at (0 comma 1) and the graph cuts the x axis at (negative 0 point 5 comma 0) and (0 point 5 comma 0).

Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. The parabola opens upwards and has a vertex at (negative 1 comma 0) and cuts the y axis at (0 comma 1).

Explanation

A cubic function typically has an S-shaped curve with a point of inflection, where the curve changes concavity. Choice B describes an increasing curve with an inflection point at (0, 1), which is characteristic of a cubic. Choice A is linear, C is an absolute-value graph, and D is a quadratic parabola.

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