Question

a. select the correct graph of the given function.
$f(x)=\

$$\begin{cases}x\\text{ if }x < 0 \\\\ 2\\text{ if }x\\geq0\\end{cases}$$

$
o a)
o b)

Explanation:

Step1: Analyze \(x < 0\) part

For \(x<0\), \(y = f(x)=x\). This is a straight - line with a slope of 1. The line starts from negative infinity on the left - hand side of the \(y\) - axis and has an open - circle at \(x = 0\) (since \(x<0\)).

Step2: Analyze \(x\geq0\) part

For \(x\geq0\), \(y = f(x)=2\). This is a horizontal line at \(y = 2\) starting from \(x = 0\) (with a closed - circle at \(x = 0\) because \(x\) can be 0 for this part of the function).

Answer:

B. Option Text (assuming option B is the graph that has a line \(y=x\) for \(x < 0\) with an open - circle at \(x = 0\) and a horizontal line \(y = 2\) for \(x\geq0\) with a closed - circle at \(x = 0\))