Final answer:
To check if a relation is a function, use Desmos to plot the graph and apply the Vertical Line Test. If any vertical line intersects the graph at more than one point, it's not a function. Relations where every x-value has one unique y-value are functions.
Step-by-step explanation:
To determine whether a relation is a function, you can utilize graphical tools like Desmos. A relation is a function if every input (usually the x-value) has exactly one output (usually the y-value). This can be visualized using the Vertical Line Test. If you draw vertical lines through the graph and any of these lines touch the graph at more than one point, the relation is not a function. This is because there are multiple outputs for a single input, which violates the definition of a function.
For instance, if we plot the relation y = x^2, every x-value corresponds to exactly one y-value, making this a function. However, if we plot y^2 = x (which describes a circle), some x-values will correspond to more than one y-value, indicating this is not a function.
When working with equations, you can solve for y in terms of x to aid in this visualization. With Desmos, you can easily input the equation and see if it passes the Vertical Line Test. This is an important skill, as understanding whether a relation is a function is fundamental in mathematical modeling and analysis in various fields, including economics.