Question

watch the video and then solve the problem given below. click here to watch the video. graph the piece - wise - defined function. f(x) = { - 1 - x if x≤2, - 4 + 2x if x>2 } choose the correct graph. a. b. c. d.

Explanation:

Step1: Analyze \(y = - 1 - x\) for \(x\leq2\)

When \(x = 2\), \(y=-1 - 2=-3\). The slope of \(y=-1 - x\) is \(- 1\) and the \(y\) - intercept is \(-1\). The graph of \(y=-1 - x\) for \(x\leq2\) is a line segment with a closed - circle at the point \((2,-3)\) (because \(x = 2\) is included in the domain \(x\leq2\)).

Step2: Analyze \(y=-4 + 2x\) for \(x>2\)

When \(x = 2\), \(y=-4+2\times2 = 0\). The slope of \(y=-4 + 2x\) is \(2\) and the \(y\) - intercept is \(-4\). The graph of \(y=-4 + 2x\) for \(x>2\) is a line with an open - circle at the point \((2,0)\) (because \(x = 2\) is not included in the domain \(x>2\)).

Answer:

(Without seeing the actual options, we can't provide a specific letter - choice answer. But the correct graph should have a line \(y=-1 - x\) with a closed - circle at \((2,-3)\) for \(x\leq2\) and a line \(y=-4 + 2x\) with an open - circle at \((2,0)\) for \(x>2\))