Question

graph the following linear function. give the domain and range. identify whether it is a constant function.\\( f(x)=x + 2 \\)\\( \dots \\)\
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\
\\( \boldsymbol{\checkmark} \\) the domain in interval notation is \\( (-\infty, \infty) \\)\
( type your answer in interval notation. )\
\\( \boldsymbol{\circ} \\) 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. )\
what is the range? select the correct choice below and fill in the answer box to complete your choice\
\\( \boldsymbol{\circ} \\) a. the range is a value or list of distinct values. \\( \\{\\} \\)\
( type an integer or a simplified fraction. use a comma to separate answers as needed. )\
\\( \boldsymbol{\circ} \\) b. the range in interval notation is \
( type your answer in interval notation. )

Explanation:

Step1: Analyze the function type

The function \( f(x) = x + 2 \) is a linear function (a first - degree polynomial function). For linear functions of the form \( f(x)=mx + b\) (where \( m = 1\) and \( b = 2\) in this case), there are no restrictions on the values of \( x\) that we can input. So, the domain (the set of all possible \( x\) - values) is all real numbers. In interval notation, this is \( (-\infty,\infty)\).

Step2: Determine the range

To find the range, we consider the output values \( y=f(x)\). Since \( y=x + 2\) and \( x\) can take any real - number value, when \( x\) approaches \( -\infty\), \( y=x + 2\) also approaches \( -\infty\), and when \( x\) approaches \( \infty\), \( y=x + 2\) also approaches \( \infty\). Also, for every real number \( y\), we can find a corresponding \( x=y - 2\) (by solving \( y=x + 2\) for \( x\)). So the range (the set of all possible \( y\) - values) is also all real numbers. In interval notation, the range is \( (-\infty,\infty)\).

Step3: Identify if it is a constant function

A constant function has the form \( f(x)=c\), where \( c\) is a constant (the function's output does not change regardless of the input \( x\)). For the function \( f(x)=x + 2\), as \( x\) changes, \( f(x)\) changes (since the slope \( m = 1
eq0\)). So it is not a constant function.

Answer:

• Domain: \((-\infty,\infty)\)
• Range: \((-\infty,\infty)\)
• It is not a constant function.