Question

Consider the following. Use the Vertical Line Test to determine whether y is a function of x. Solve for y to describe how you can use a graphing utility to produce the given graph.

Answer 1

Answer:

$\begin{gathered} a)\text{ y is not function of x} \\ b)\text{ y = }\pm\sqrt{(x-4)} \end{gathered}$

Explanation:

a) Here, we want to use the vertical line test to check if y is a function of x

To use the test, we draw a vertical line through any point on the graph. If the vertical line touches two points on the curve, then y is not a function of x

If we draw a vertical line as described, we would see that it touches two points on the curve which indicates that y is not a function of x

b) To solve for y, we proceed with the following steps:

$\begin{gathered} x\text{ - y}^2\text{ = 4} \\ y^2\text{ = x-4} \\ y\text{ = }\pm\sqrt{(x-4)} \end{gathered}$