# Determining a Function

Determining if an equation is a function is easy if we know or at least familiar of the graph of a certain equation. To determine a function, we conduct vertical line test. It is done by intersecting a vertical line anywhere in the graph of an equation being test. If the vertical line drawn intersects the equation once the equation is a function. Otherwise the equation is not a function.

Vertical Line Test Vertical Line Test

Given a line $x-y=2$ and the blue line as the vertical line drawn. As the vertical line moves from left to right It always intersects the line at only one point. It implies that the equation $x-y=2$ is a function. Same process is done with other types of equation.

Worked Problem:

Determine which of the following is/are function/s?

a. $x^2+4y^2=16$   b. $4x^2-x-2=y$    c. $x+3y-2=0$    d. $y=\sqrt{x-4}$

Solution: This topic will help us a lot to determine the graph of an equation without actually graphing it. But since I have the power to graph it using my Geogebra tool let me show how the graph of these equations look like.

a. $x^2+4y^2=16$ this is an ellipse. Ellipse

b. $4x^2-x-2=y$ c. $x+3y-2=0$ Linear equation

d. $y=\sqrt{x-4}$ Sq. Root Function

Again the equation is a function if the vertical line drawn intersects the graph of an equation being tested at only one point. All are functions except the ellipse since as we move the vertical line horizontally it intersects the graph of an ellipse at two points.

### Dan

Blogger and a Math enthusiast. Has no interest in Mathematics until MMC came. Aside from doing math, he also loves to travel and watch movies.