Question

question
graph the piece - wise function given below.
f(x)=\begin{cases}|x|&\text{for }x < 2\\-4&\text{for }x>5end{cases}
step 1: select a function then move with blue dot (if necessary)

Explanation:

Step1: Analyze \(y = |x|\) for \(x<2\)

The absolute - value function \(y = |x|\) is defined as \(y=-x\) for \(x < 0\) and \(y = x\) for \(x\geq0\). We only consider the part of \(y = |x|\) where \(x<2\). When \(x = 0\), \(y = 0\); when \(x=- 2\), \(y = 2\); when \(x = 2\), this part of the function is not defined (open - circle at \(x = 2\)).

Step2: Analyze \(y=-4\) for \(x > 5\)

This is a horizontal line. For all \(x\) values greater than \(5\), \(y=-4\). When \(x = 5\), this part of the function is not defined (open - circle at \(x = 5\)).

Step3: Graph the function

Graph \(y = |x|\) for \(x<2\) as a 'V' - shaped graph with an open - circle at \((2,2)\). Then graph \(y=-4\) for \(x > 5\) as a horizontal line with an open - circle at \((5,-4)\). There is no definition for the function in the interval \([2,5]\).

Answer:

Graph \(y = |x|\) with an open - circle at \((2,2)\) for \(x<2\) and graph \(y=-4\) with an open - circle at \((5,-4)\) for \(x > 5\).