Functions and Their Inverses — Test

Question 13 • Math 3

How is the graph of y is equal to open paren x minus 1 close paren squared minus 3 transformed to produce the graph of y is equal to 1 half times open paren x plus 4 close paren squared ?

Answer

The graph is stretched horizontally by a factor of 1 half , translated left 5 units, and translated down 3 units.

The graph is translated left 5 units, compressed vertically by a factor of 1 half , and translated up 3 units.

The graph is stretched vertically by a factor of 1 half , translated left 5 units, and translated up 3 units.

The graph is translated left 5 units, compressed horizontally by a factor of 1 half , and translated down 3 units.

Explanation

The starting parabola has vertex (1, −3), while the target has vertex (−4, 0). Moving the vertex from (1, −3) to (−4, 0) translates the graph 5 units left and 3 units up. The target’s coefficient of 1/2 makes it a vertical compression by a factor of 1/2, so the correct choice is B.

AI-written and checked against the verified answer.

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