## College Algebra (11th Edition)

The parent function is $f(x)=\vert x\vert$ (with red), but the graph of $g(x)=\vert -\frac{1}{3} x\vert$ (with blue) will be wider, as the coefficient multiplies each y-value of the parent function by $-\frac{1}{3}$ However, it will not be reflected across the y-axis, as the minus sign is inside the absolute value sign. For drawing the exact graph of the parent function here is a table of values: $f(-2)=\mid -2\mid=2$ $f(-1)=\mid -1\mid=1$ $f(0)= \mid 0\mid=0$ $f(1)= \mid 1\mid=1$ $f(2)= \mid 2\mid=2$ By the use of graph transformation techniques, the graph is horizontally stretched by a factor of $3$. For drawing the exact graph of $g(x)$ here is the table of values of the given function: $g(-3)=\mid -\frac{1}{3}\times -3\mid=1$ $g(-1)=\mid -\frac{1}{3}\times -1\mid=\frac{1}{3}$ $g(0)=\mid -\frac{1}{3}\times 0\mid=0$ $g(1)=\mid -\frac{1}{3}\times1\mid=\frac{1}{3}$ $g(3)=\mid -\frac{1}{3}\times 3\mid=1$