Question

multiple choice 10 points
for the piecewise function shown below, which of the following is the correct graph?
f(x) = {x + 1 if x < 1; 4 if x ≥ 1}

Explanation:

Step1: Analyze first - part of function

For \(y = x + 1\) when \(x<1\), it is a linear - function with slope \(m = 1\) and \(y\) - intercept \(b = 1\). The graph is a line with an open - circle at the point \((1,y)\) where \(y=1 + 1=2\) (since \(x<1\)).

Step2: Analyze second - part of function

For \(y = 4\) when \(x\geq1\), it is a horizontal line. The graph is a horizontal line \(y = 4\) with a closed - circle at the point \((1,4)\) (since \(x\geq1\)).

Answer:

Without the actual multiple - choice options provided, we can't select a specific answer. But the graph should have a line \(y=x + 1\) for \(x<1\) (open - circle at \((1,2)\)) and a horizontal line \(y = 4\) for \(x\geq1\) (closed - circle at \((1,4)\)).