What Determines the Range of a Rational Function Like f(x) = 2/(x - 3)?

In summary, the range of f(x) = 2/(x - 3) is all the values the function can take on over its domain. To find the range, we can also look at the values of 3 and 0 in both the function and its inverse. The easiest way to find the range may vary depending on the function.
  • #1
mathdad
1,283
1
Find the range of
f(x) = 2/(x - 3).

1. What exactly are we looking for when we say RANGE of a rational function?

2. Is the domain of the inverse the range of the given function?

3. What is the easiest way to find the range? Graphing?
 
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  • #2
1. All the values a function assumes over its domain.

2. Let's see:

y = 2/(x - 3)

x - 3 = 2/y

x = 2/y + 3

y^(-1) = 2/x + 3

What conclusions may we draw? (look at the values 3 and 0 in both functions).

3. Depends on the function (in my opinion).
 
  • #3
greg1313 said:
1. All the values a function assumes over its domain.

2. Let's see:

y = 2/(x - 3)

x - 3 = 2/y

x = 2/y + 3

y^(-1) = 2/x + 3

What conclusions may we draw? (look at the values 3 and 0 in both functions).

3. Depends on the function (in my opinion).

I do not understand your answer to question 1.
I also do know what conclusions we can draw based on the values of 3 and 0 in both functions.
 

FAQ: What Determines the Range of a Rational Function Like f(x) = 2/(x - 3)?

What is a rational function?

A rational function is a mathematical function that can be written as the quotient of two polynomial functions. It is a type of algebraic function that includes variables in both the numerator and denominator.

What is the domain of a rational function?

The domain of a rational function is all the possible values that the independent variable (x) can take without making the denominator equal to zero. In other words, it is the set of all real numbers except the values that would result in division by zero.

How do you find the range of a rational function?

To find the range of a rational function, you need to first determine the domain. Then, you can use algebraic techniques such as factoring, graphing, or solving for the dependent variable (y) to determine the corresponding range of values.

What are the common features of the graph of a rational function?

The common features of the graph of a rational function include a horizontal and/or vertical asymptote, a point of discontinuity, and a curve that may approach but never touch the asymptotes. The graph may also have holes or gaps at the points of discontinuity.

How do rational functions relate to real-world situations?

Rational functions can be used to model real-world situations that involve quantities that are dependent on each other. For example, they can be used to represent rates of change, such as velocity, growth, or decay. They are also commonly used in engineering, physics, and economics to solve problems involving varying quantities.

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