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Algebra Question: What are the differences among expressions,
Resolved Question:
Algebra Question:
What are the differences among expressions, equations and functions? Provide examples of each. (provide detailed insight and mathematical examples to answer these)
Submitted:
2 years ago.
Category:
PreCalculus
Expert:
Ryan
replied 2 years ago.
Hi,
Thank you for using JustAnswer.
An algebraic
expression
is a collection of numbers, variables, and operators (addition, subtraction, multiplication, division, exponentiation, etc) which represent some value.
For example, the following are expressions:
3 + 4 (which represents the value 7)
x + y (which represents the sum of the values of the variables x and y)
5x (which represents the product of 5 and the value of the variable x)
x/y (which represents the quotient of the value of the variable x and the value of the variable y)
An
equation
is a pair of expressions which are connected by an equal sign (=). An equation states that the expression on one side of the equal sign has the same value as the expression on the other side.
For example, the following are equations:
x = 3
x + y = 4
a² + b² = c²
k = 5a²/b
A
function
is a particular type of equation. A function relates the value of an independent variable, typically denoted as "x", to the value of a dependent variable, typically denoted as "y" or "f(x)" (which is shorthand notation for "function of x"). While this is very similar to the concept of an equation, a function speaks more to the idea of an input value leading to an output value.
One distinguishing characteristic of a function is that there can be one, and only one, output value for any individual input value. For this reason, an equation such as y = √(16  x)² (which is the equation of a circle) is not a function, because for almost every value of x where the function is defined there are two possible values of y.
Examples of functions include:
y = mx + b
f(x) = x²
y = 3x³ + x² + 4x + 6
g(x) = log (x)
Please feel free to ask if you have any additional questions about this.
Thanks,
Ryan
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