For the function, tell whether the graph opens up or opens down, identify the vertex, and tell whether the graph is wider, narrower, or the same width as the graph of y = |x|.

y = 2|x – 1| - 3

opens up, (1, 3), wider

opens up, (1, 3), narrower

opens up, (-1, -3), wider

opens up, (1, -3), narrower

The factor of +2 multiplying the function tells you the graph is expanded vertically by a factor of 2. The parent function opens upward, and the positive sign on this expansion factor does not change that. The expansion means that y-values will be farther from the vertex for the same x-value distance from the vertex. This give the appearance of a narrower graph.

As always, the transformation ...

f(x -h) +k

moves the vertex from (0, 0) to (h, k). Here, you have (h, k) = (1, -3), so that is the location of the vertex of the transformed function.

For the function, tell whether the graph opens up or opens down, identify the vertex, and tell whether the graph is wider, narrower, or the same width as the graph of y = |x|. y = 2|x – 1| - 3 opens up, (1, 3), wider opens up, (1, 3), narrower opens up, (-1, -3), wider opens up, (1, -3), narrower

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