How does an equation represent a function

Study now. See Answer. Best Answer. Hope it helped! Study guides. Algebra 20 cards. A polynomial of degree zero is a constant term. The grouping method of factoring can still be used when only some of the terms share a common factor A True B False. The sum or difference of p and q is the of the x-term in the trinomial. A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials.

Multiplication chart! Math and Arithmetic 20 cards. The length of a rectangular floor is 2 feet more than its width The area of the floor is square feet Kim wants to use a rug in the middle of the room and leave a 2 foot border of the floor visib. The perimeter of a rectangle is 18 feet and the area of the rectangle is 20 square feet what is the width of the rectangle. The sum of two numbers is 19 and their product is 78 What is the larger number.

A rectangular garden has a perimeter of 48 cm and an area of sq cm What is the width of this garden. Q: How does an equation represent a function?

Write your answer Related questions. Does equation y 2 plus 1 represent a linear function? What information does the graph of a function provide with respect to the algebraic equation? Does the equation y equals 2x plus 1 represent a function? Is the linear equation X equals a function? How can a linear equation represent a function? What is necessary and sufficient condition in respect to mathematics and economics?

What are 4 ways to represent a function? Which equation could represent the area of a square as a function of a side? In a chemical equation the coefficients represent the what? What does the answer to an equation represent?

What are 3 ways other than words to represent a function? There are different percent numbers we could get but only about five possible letter grades, so there cannot be only one percent number that corresponds to each letter grade.

As we have seen in some examples above, we can represent a function using a graph. Graphs display a great many input-output pairs in a small space. The visual information they provide often makes relationships easier to understand. By convention, graphs are typically constructed with the input values along the horizontal axis and the output values along the vertical axis.

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 corresponding output value. The vertical line test can be used to determine whether a graph represents a function. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because a function has only one output value for each input value.

Howto: Given a graph, use the vertical line test to determine if the graph represents a function. If any vertical line intersects a graph more than once, the relation represented by the graph is not a function.

From this we can conclude that these two graphs represent functions. Once we have determined that a graph defines a function, an easy way to determine if it is a one-to-one function is to use the horizontal line test. Draw horizontal lines through the graph. If any horizontal line intersects the graph more than once, then the graph does not represent a one-to-one function. Howto: Given a graph of a function, use the horizontal line test to determine if the graph represents a one-to-one function.

Are either of the functions one-to-one? Any horizontal line will intersect a diagonal line at most once. In this text, we will be exploring functions—the shapes of their graphs, their unique characteristics, their algebraic formulas, and how to solve problems with them. When learning to read, we start with the alphabet.

When learning to do arithmetic, we start with numbers. When working with functions, it is similarly helpful to have a base set of building-block elements. Some of these functions are programmed to individual buttons on many calculators.

We will see these toolkit functions, combinations of toolkit functions, their graphs, and their transformations frequently throughout this book. It will be very helpful if we can recognize these toolkit functions and their features quickly by name, formula, graph, and basic table properties.

Jay Abramson Arizona State University with contributing authors. Learning Objectives Determine whether a relation represents a function. Find the value of a function.

Determine whether a function is one-to-one. Use the vertical line test to identify functions. Graph the functions listed in the library of functions.

In this case, each input is associated with a single output. Function A function is a relation in which each possible input value leads to exactly one output value. How To: Given a relationship between two quantities, determine whether the relationship is a function Identify the input values. Identify the output values. If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.

Is price a function of the item? Is the item a function of the price? The output values are then the prices. Two items on the menu have the same price. If we consider the prices to be the input values and the items to be the output, then the same input value could have more than one output associated with it. Therefore, the item is a not a function of price. Percent grade 0—56 57—61 62—66 67—71 72—77 78—86 87—91 92— Grade point average 0.

Is the player name a function of the rank? Answer a Yes Answer b yes. Using Function Notation Once we determine that a relationship is a function, we need to display and define the functional relationships so that we can understand and use them, and sometimes also so that we can program them into computers.

Solution Using Function Notation for Days in a Month Use function notation to represent a function whose input is the name of a month and output is the number of days in that month. Analysis Note that the inputs to a function do not have to be numbers; function inputs can be names of people, labels of geometric objects, or any other element that determines some kind of output.

Representing Functions Using Tables A common method of representing functions is in the form of a table. Check to see if each input value is paired with only one output value. If so, the table represents a function. Finding Input and Output Values of a Function When we know an input value and want to determine the corresponding output value for a function, we evaluate the function.

Evaluation of Functions in Algebraic Forms When we have a function in formula form, it is usually a simple matter to evaluate the function. How To: Given the formula for a function, evaluate.

Given the formula for a function, evaluate. Replace the input variable in the formula with the value provided. Calculate the result. Evaluating Functions Expressed in Formulas Some functions are defined by mathematical rules or procedures expressed in equation form.

Solve the equation to isolate the output variable on one side of the equal sign, with the other side as an expression that involves only the input variable.

Use all the usual algebraic methods for solving equations, such as adding or subtracting the same quantity to or from both sides, or multiplying or dividing both sides of the equation by the same quantity.

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