Question

If the parent function is y = x, explain the transformation(s) that occur to get from

the parent function to y = 3(x - 5) – 2

Answer 1

Going from y = x to y = 3x means we have vertically stretched everything by a factor of 3. For example, the point (4,4) moves to (4,12).

Then we replace x with (x-5) so that we get to y = 3(x-5). This shifts the graph 5 units to the right.

Finally, the -2 at the end shifts everything down 2 units.

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Summary:

We applied these three transformations

• Vertically stretch by a factor of 3
• Shift 5 units to the right.
• Shift 2 units down