Find the domain of each function. a. h(x)=3 x+6 b. f(x)=(1)/(x-4)

Name: Problem 79, Chapter 2: Intermediate Algebra
Uploaded: 2020-08-03T22:25:15-08:00
Duration: 1 min 34 s
Channel: Dale Sanford
Description: Find the domain of each function. a. h(x)=3 x+6 b. f(x)=(1)/(x-4)

step 1 Let's find the domain of our function H of x equals 3x plus 6. So to find the domain, we have to

Find the domain of each function. a. h(x)=3 x+6 b....

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Key Concepts

Excluded Values

Excluded values are specific input values that must be omitted from the function's domain because they result in undefined expressions, such as when a denominator becomes zero. Recognizing and excluding these values is crucial when determining the domain, especially in functions that involve fractions or radicals.

Rational Function

A rational function is a function that can be expressed as the ratio of two polynomials. Its domain includes all real numbers except those that cause the denominator to be zero, since division by zero is undefined. Determining the domain of a rational function involves finding and excluding these particular values.

Function Domain

The domain of a function refers to the set of all possible input values (usually x-values) for which the function is defined. Understanding the domain is essential because it tells us which values we can plug into the function without causing undefined or problematic expressions.

Linear Function

A linear function is typically expressed in the form f(x) = mx + b, where m and b are constants. Linear functions are defined for all real numbers because they do not involve division by a variable, square roots, or other operations that impose restrictions on the input.

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