Question

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)?

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