The graph of an absolute value function has a vertex at (–2, 3) and passes through the point (–1, 0). Using transformations of the parent function, has the graph been dilated by a scale factor other than 1? Explain.

Answer:

Yes, the graph has been dilated by a scale factor of 3. To determine this, use the standard form of an absolute value function, y = a|x – h| + k, where (h, k) is the vertex. Substituting the vertex (-2, 3) and the point (-1, 0) into the equation gives 0 = a|(-1) – (-2)| + 3. Simplifying this results in 0 = a(1) + 3, which means a = –3. Since the absolute value of a is 3 (not 1), the graph has undergone a vertical stretch (dilation).