Question

graph the following function by moving the green and blue dots (if necessary). y = \frac{1}{3}|x| start over

Explanation:

Step1: Analyze when x≥0

When \(x\geq0\), \(y = \frac{1}{3}x\). We can find points on this part of the graph. For example, when \(x = 3\), \(y=\frac{1}{3}\times3 = 1\); when \(x = 6\), \(y=\frac{1}{3}\times6=2\).

Step2: Analyze when x<0

When \(x<0\), \(y=\frac{1}{3}(-x)=-\frac{1}{3}x\). For example, when \(x=-3\), \(y =-\frac{1}{3}\times(-3)=1\); when \(x = - 6\), \(y=-\frac{1}{3}\times(-6) = 2\).

Step3: Plot the points

Plot the points obtained from the above - two steps on the coordinate - plane and connect them to form the V - shaped graph of the absolute - value function \(y=\frac{1}{3}|x|\). The vertex of the graph is at the origin \((0,0)\) since when \(x = 0\), \(y=\frac{1}{3}\times|0|=0\).

Answer:

The graph is a V - shaped graph with the vertex at the origin \((0,0)\). For \(x\geq0\), it is a straight - line with a slope of \(\frac{1}{3}\), and for \(x<0\), it is a straight - line with a slope of \(-\frac{1}{3}\).