Consider the two functions, f(x) and g(x), shown below, which will have two transformations: vertical translation and vertical stretch. [br][br]f(x) will be stretched first, followed by a translation.[br]g(x) will be translated first, followed by a stretch.[br][br]Play around with this, and then answer the questions below.

[b]Question 1: [/b]Does the order of vertical translations and vertical stretches affect each other?[br][br][b]Question 2: [/b]Consider a vertical stretch by a factor of 2, and a vertical translation up 1 unit. Find the equation for f(x) and g(x). Are they equal?[br][br][b]Question 3: [/b]Consider a vertical reflection, and a vertical translation up 2 units. Find the equation for f(x) and g(x). Are they equal?[br][br][b]Question 4: [/b]Generalize: Consider a vertical stretch by a factor of a, and a vertical translation up d units. Find the equation for f(x) and g(x).[br][br][b]Question 5: [/b]Consider the equation h(x)=[math]3x^2-12[/math]. Write the two transformations required to transform f(x)=[math]x^2[/math] to h(x) if:[br] [b]A: [/b] We do a stretch first;[br][br][b] B: [/b]We do a translation first.[br][br]