Table of Contents

## How do you determine if an equation is a function?

Determining whether a relation is a function on a graph is relatively easy by using the vertical line test. If a vertical line crosses the relation on the graph only once in all locations, the relation is a function. However, if a vertical line crosses the relation more than once, the relation is not a function.

**What is the functional form of an equation?**

Form of the equation of a line in which the y-coordinate is expressed as a function of the other variables, that is y = mx + b, where m is the slope of the line and b is its y-intercept. This particular form is also called the “slope-intercept form”.

### What is F 2 )?

A function is an equation that has only one answer for y for every x. It is common to name a function either f(x) or g(x) instead of y. f(2) means that we should find the value of our function when x equals 2.

**Why do we use F X instead of Y?**

Now when we write f(x), we mean that we want the machine to take a value “x” and transform it to an output. If we want to then see this visually as an X-Y plot for other values of x, then we would say that the Y-axis represents f(x) for all values of “x” on the X-axis. So, then you have y = f(x).

#### What equations are not functions?

Vertical lines are not functions. The equations y=±√x and x2+y2=9 are examples of non-functions because there is at least one x-value with two or more y-values.

**Where are functional equations used?**

It is often useful to prove surjectivity or injectivity and prove oddness or evenness, if possible. It is also useful to guess possible solutions. Induction is a useful technique to use when the function is only defined for rational or integer values.

## How do you choose functional form?

One way to select the functional form is to use a general-to-specific methodology: Estimate a very general nonlinear form and, through hypothesis testing, determine whether it is possible to pare down the model to a more specific form.

**What is not a function equation?**

Horizontal lines are functions that have a range that is a single value. Vertical lines are not functions. The equations y=±√x and x2+y2=9 are examples of non-functions because there is at least one x-value with two or more y-values.