Which statement best illustrates using the vertical line test to determine if the graph below is a function of x? On a coordinate plane, a circle is centered around (0, 0).
Answers
Step-by-step explanation:
As we have seen in some examples above, we can represent a function using a graph. Graphs display a great many input-output pairs in a small space. The visual information they provide often makes relationships easier to understand. By convention, graphs are typically constructed with the input values along the horizontal axis and the output values along the vertical axis.
The most common graphs name the input value \displaystyle xx and the output value \displaystyle yy, and we say \displaystyle yy is a function of \displaystyle xx, or \displaystyle y=f\left(x\right)y=f(x) when the function is named \displaystyle ff. The graph of the function is the set of all points \displaystyle \left(x,y\right)(x,y) in the plane that satisfies the equation \displaystyle y=f\left(x\right)y=f(x). If the function is defined for only a few input values, then the graph of the function is only a few points, where the x-coordinate of each point is an input value and the y-coordinate of each point is the corresponding output value. For example, the black dots on the graph in Figure 11 tell us that \displaystyle f\left(0\right)=2f(0)=2 and \displaystyle f\left(6\right)=1f(6)=1. However, the set of all points \displaystyle \left(x,y\right)(x,y) satisfying \displaystyle y=f\left(x\right)y=f(x) is a curve. The curve shown includes \displaystyle \left(0,2\right)(0,2) and \displaystyle \left(6,1\right)(6,1) because the curve passes through those points.