In mathematics, the graph of a function is the set of ordered pairs , where In the common case where and are real numbers, these pairs are Cartesian coordinates of points in a plane and often form a curve. The graphical representation of the graph of a function is also known as a plot.

We typically construct graphs with the input values along the horizontal axis and the output values along the vertical axis. The most common graphs name the input value x x and the output value y y, and we say y y is a function of x x, or y = f (x) y = f (x) when the function is named f f.

Graphing functions is the process of drawing the graph (curve) of the corresponding function. Graphing basic functions like linear, quadratic, cubic, etc is pretty simple, graphing functions that are complex like rational, logarithmic, etc, needs some skill …

Determine whether a relation represents a function. Find function values. Determine whether a function is one-to-one. Use the vertical line test to identify functions. Graph the functions in the library of functions. A jetliner changes altitude as its distance from the starting point of …

Mar 4, 2025 · (function graph analysis, mathematical functions, graph interpretation) What Makes a Graph a Function? A graph represents a function if each input (usually the x-value) corresponds to exactly one output (the y-value). This is known as the vertical line test. If you can draw a vertical line anywhere on the graph and it intersects the curve at ...

The graph of a function is the collection of all ordered pairs of the function. These are usually represented as points in a Cartesian coordinate system. As an example, consider the function.

Jan 29, 2025 · In short, if you draw a vertical line through a graph and hit only ONE point, then that graph represents a function. In the example we just showed, if you draw a vertical line through the domain value of -2, the line will pass through range values of 2 and -2. Therefore, the relation fails the vertical line test.

Apr 21, 2025 · Furthermore, the graph is a function because for each \(x\)-value there is only one corresponding \(y\)-value. In fact, any nonvertical or nonhorizontal line is a function with domain and range consisting of all real numbers. Any graph is a set of ordered pairs and thus defines a relation. Consider the following graph of a circle:

Oct 25, 2024 · Graphs of functions are visual representations of how one quantity depends on another. In simple terms, a graph shows the relationship between two variables: one variable is usually on the horizontal axis (called the x-axis), and the other is …

5 days ago · The graph of the function is the set of all points \( (x,y) \) in the plane that satisfies the equation \( y=f(x) \). 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 ...