Question

determine whether the graph represents a function. if it does represent a function, give its domain and range.
yes
what is the domain? select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. (type an inequality or a compound inequality)
b. the domain is all real numbers
c. the graph does not represent a function
what is the range? select the correct choice below and, if necessary, fill in the answer box to complete your choice
a. (type an inequality or a compound inequality)
b. the range is all real numbers
c. the graph does not represent a function

Explanation:

Step1: Use the vertical line test

A graph represents a function if any vertical line drawn intersects the graph at most once. For a straight - line graph (non - vertical), it passes the vertical line test. Since this is a non - vertical straight line, it is a function.

Step2: Determine the domain

The domain of a linear function (a non - vertical straight line) is all real numbers. Because for any real number \(x\), we can find a corresponding \(y\) value on the line.

Step3: Determine the range

The range of a linear function (a non - vertical straight line) is all real numbers. As \(x\) takes on all real values, \(y = mx + b\) (where \(m
eq0\)) also takes on all real values.

Answer:

For the domain: B. The domain is all real numbers.
For the range: B. The range is all real numbers.