Question

graph the piece - wise - defined function f(x)={x - 3 if x≤5, 2 if x>5}. choose the correct graph. a. b. c. d.

Explanation:

Step1: Analyze \(f(x)=x - 3\) for \(x\leq5\)

The equation \(y=x - 3\) is a linear - function with slope \(m = 1\) and \(y\) - intercept \(b=-3\). When \(x = 5\), \(y=5 - 3=2\). The graph of \(y=x - 3\) for \(x\leq5\) is a line segment with a closed - circle at the end - point \((5,2)\) (because \(x = 5\) is included in the domain \(x\leq5\)).

Step2: Analyze \(f(x)=2\) for \(x>5\)

The equation \(y = 2\) for \(x>5\) is a horizontal line. It has an open - circle at the point \((5,2)\) (since \(x = 5\) is not included in the domain \(x>5\)) and extends to the right.

Answer:

(Without seeing the actual graphs A, B, C, D, we can't give a specific letter - choice answer. But the correct graph should have a line \(y=x - 3\) with a closed - circle at \((5,2)\) for \(x\leq5\) and a horizontal line \(y = 2\) with an open - circle at \((5,2)\) for \(x>5\).)