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Chapter 1: Problem 113

What is the graph of a function?

Short Answer

Expert verified
The graph of a function represents all the ordered pairs that comprise a function. It is drawn by plotting all pairs (x, y) satisfying the function equation on a cartesian grid and then joining these points to form a curve or line.

Step by step solution

01

Definition

A function is a relationship between two sets of numbers (usually called the domain and the range) that assigns to each member of the domain exactly one member of the range. The graph of a function f is the set of points in the plane whose coordinates (x, y) satisfy the equation y=f(x). This means each x-value is paired with exactly one y-value.
02

Graphing a Function

To graph a function, start by choosing a number for x, then calculate the corresponding value of y using the provided function. Repeat this process for various x-values and then plot these points (x, y) on a cartesian grid.
03

Visual Representation of the Function

After plotting all the points, they can be joined to form a continuous curve or line. The resulting graph represents all possible pairs of (x, y) that satisfy the function equation.

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Most popular questions from this chapter

Will help you prepare for the material covered in the next section. Find the ordered pairs \((\quad, 0)\) and \((0, \quad)\) satisfying \(4 x-3 y-6=0\).

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