Finding the Domain of an Algebraic Function

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In summary, the domain of the function f(x) = 2/(x + 3) is all real numbers except -3. This is because -3 would make the denominator 0, which is undefined. Therefore, the domain can be written as (-∞, -3) U (-3, ∞).
  • #1
NelsonsXanadu
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Homework Statement



Find the Domain

f(x) = ___2___
x+3

Homework Equations





The Attempt at a Solution

I know this is a pretty simple question just want to make sure I'm on the right track. Wouldn't the domain be all numbers except zero? Because you can't divide by zero? How would I write this
 
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  • #2
NelsonsXanadu said:

Homework Statement



Find the Domain

f(x) = ___2___
x+3
Another way to write this that is clearer is f(x) = 2/(x + 3)
NelsonsXanadu said:

The Attempt at a Solution

I know this is a pretty simple question just want to make sure I'm on the right track. Wouldn't the domain be all numbers except zero? Because you can't divide by zero? How would I write this
No, 0 is in the domain, because f(0) = 2/(0 + 3) = 2/3.
Yes, you cannot divide by zero. What value of x makes the denominator 0?
 
  • #3
Well a -3 would make the denominator 0...
 
  • #4
So -3 is not in the domain. Are there any other values for which this function is undefined?
 
  • #5
What you are looking for is for the *denominator* to not be zero, such that you don't divide by zero. And you're right in saying that -3 is not in the domain. Just make sure that -3 is the only thing that's not in the domain.
 

1. What is an algebraic function?

An algebraic function is a mathematical function that can be expressed using a combination of algebraic operations, such as addition, subtraction, multiplication, and division, as well as exponents and roots. It is used to describe the relationship between two or more variables.

2. How is an algebraic function different from other types of functions?

An algebraic function is different from other types of functions, such as trigonometric or exponential functions, because it is composed of only algebraic operations. Other types of functions may involve trigonometric, logarithmic, or exponential operations.

3. What is the standard form of an algebraic function?

The standard form of an algebraic function is y = f(x), where y represents the output or dependent variable, x represents the input or independent variable, and f(x) is the expression that defines the relationship between the two variables.

4. How do you graph an algebraic function?

To graph an algebraic function, you can plot points on a coordinate plane by substituting different values for the input variable and solving for the corresponding output variable. You can also use transformations, such as translations and reflections, to graph more complex algebraic functions.

5. What are some real-life applications of algebraic functions?

Algebraic functions are used in various fields, such as physics, economics, and engineering, to model and solve real-world problems. For example, they can be used to calculate the trajectory of a projectile, determine the optimal production level for a company, or design a bridge that can withstand certain conditions.

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