Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line.
-$$y = 2 x ^ { 3 } + 3$$

Question

Quizplus · Accepted Answer

To graph the equation $y = 2x^3 + 3$, we start at the point $(0, 3)$ and then use the slope to determine other points on the graph. The graph is a solid line because the relation is not a function, meaning that for some $x$ values, there are two $y$ values.

To find the inverse of the relation, we swap $x$ and $y$ and solve for $y$. 
$$x = 2y^3 + 3 \implies 2y^3 = x - 3 \implies y = \sqrt[3]{\frac{x-3}{2}}$$
To graph the inverse, we use the same points as before, but swap the $x$ and $y$ coordinates. The graph is a dashed line because it is the inverse of a non-function relation (so it is also non-function).

The best choice is (C) because it correctly shows the solid graph of $y=2x^3+3$ and the dashed graph of its inverse.

Graph the Equation of the Relation Using a Solid Line y=2x3+3y = 2 x ^ { 3 } + 3y=2x3+3

Graph the Equation of the Relation Using a Solid Line $y = 2 x ^ { 3 } + 3$