7a: Let f (x) = 4x. The graph of f (x) is transformed into the graph g (x) by a vertical stretch of 2 units and a translation of 5 units right. What is the equation for g (x) ?

7b: Let h (x) = 10x. The graph of h (x) is transformed into the graph of g (x) by a vertical compression of 1/2 and a translation of 3 units up. What is the equation for g (x) ?

Question

Mathematics

Dane Kirk

7 January, 09:09

7a: Let f (x) = 4x. The graph of f (x) is transformed into the graph g (x) by a vertical stretch of 2 units and a translation of 5 units right. What is the equation for g (x) ?

7b: Let h (x) = 10x. The graph of h (x) is transformed into the graph of g (x) by a vertical compression of 1/2 and a translation of 3 units up. What is the equation for g (x) ?

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Answers (1)

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Marlene Noble · Answer 1

Vertical stretch means y values are multiplied by 2, so 2f (x).

Translation of 5 units to the right, means x values minus 5 (it does the opposite to what you might think)

So overall g (x) = 2f (x-5) = 2 (4 (x-5)) = 8 (x-5) = 8x-40

Vertical compression means y values are halved

3 units up mean y values plus 3

So ½h (x) + 3 = g (x) = ½ (10x) + 3 = 5x + 3