Question

match the function with its graph.
$f(x)=x + 2$ for $x < 1$

Explanation:

Step1: Analyze the function at \(x = 1\)

Since \(x<1\), when \(x = 1\) is approached from the left, the point at \(x = 1\) is not included. So, there should be an open - circle at \(x = 1\).

Step2: Analyze the \(y\) - value for \(x\) near \(1\)

Substitute \(x = 1\) into \(y=x + 2\), we get \(y=1+2=3\).

Step3: Analyze the general form of the line

The function \(y=x + 2\) is a straight line with slope \(m = 1\) and \(y\) - intercept \(b=2\).

Answer:

The third graph (with an open - circle at \((1,3)\) and a line \(y=x + 2\) for \(x<1\)) is the correct match.