Question

graph this function.

$y = |x|$

click to plot the vertex first.

Explanation:

Step1: Identify the vertex of \( y = |x| \)

The absolute - value function \( y = |x| \) can be written as \( y=

$$\begin{cases}x, & x\geq0\\-x, & x < 0\end{cases}$$

\). The vertex of the absolute - value function \( y = |x - h|+k \) is at the point \( (h,k) \). For \( y = |x| \), \( h = 0 \) and \( k = 0 \), so the vertex is at the point \( (0,0) \).

Step2: Find other points to graph the function

• When \( x = 1 \), \( y=|1| = 1 \), so the point \( (1,1) \) is on the graph.
• When \( x=- 1 \), \( y = |-1|=1 \), so the point \( (-1,1) \) is on the graph.
• When \( x = 2 \), \( y=|2| = 2 \), so the point \( (2,2) \) is on the graph.
• When \( x=-2 \), \( y = |-2| = 2 \), so the point \( (-2,2) \) is on the graph.

To graph the function, first plot the vertex \( (0,0) \). Then, for the part of the graph where \( x\geq0 \), use the slope of 1 (since \( y = x \) for \( x\geq0 \)) and plot points like \( (1,1) \), \( (2,2) \), etc. For the part of the graph where \( x < 0 \), use the slope of - 1 (since \( y=-x \) for \( x < 0 \)) and plot points like \( (-1,1) \), \( (-2,2) \), etc. Then connect the points to form a V - shaped graph.

Answer:

The vertex of the function \( y = |x| \) is at the point \((0,0)\). To complete the graph, plot additional points such as \((1,1)\), \((-1,1)\), \((2,2)\), \((-2,2)\) and connect them to form a V - shaped graph with the vertex at \((0,0)\).