Question

graph the following linear function. give the domain and range. identify whether it is a constant function
f(x) = x + 2

use the graphing tool to graph the linear equation.

what is the domain? select the correct choice below and fill in the answer box to complete your choice.
a. the domain in interval notation is
(type your answer in interval notation.)
b. the domain is a value or list of distinct values,
(type an integer or a simplified fraction. use a comma to separate answers as needed.)

Explanation:

Step1: Analyze the function type

The function \( f(x) = x + 2 \) is a linear function (a polynomial function of degree 1). For linear functions (and all polynomial functions), there are no restrictions on the input values (x - values) because we can plug in any real number for \( x \) and get a valid output (y - value).

Step2: Determine the domain

The domain of a function is the set of all possible input values (x - values). Since there are no values of \( x \) that would make \( f(x)=x + 2 \) undefined (we don't have division by zero, square roots of negative numbers in real - valued functions here, etc.), the domain includes all real numbers. In interval notation, the set of all real numbers is represented as \( (-\infty, \infty) \). Also, since the domain is all real numbers (not a single value or a list of distinct values), we choose option A.

Answer:

A. The domain in interval notation is \((-\infty, \infty)\)