Consider the two functions, f(x) and g(x), shown below, which will have two transformations: horizontal translation and horizontal 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 horizontal translations and horizontal stretches affect each other?[br][br][b]Question 2: [/b]Consider a horizontal stretch by a factor of 0.5, and a horizontal translation by 4 units to the right. Find the equation for f(x) and g(x). Are they equal?[br][br][b]Question 3: [/b]Consider a horizontal reflection, and a horizontal translation by 2 units to the right. Find the equation for f(x) and g(x). Are they equal?[br][br][b]Question 4: [/b]Generalize: Consider a horizontal stretch by a factor of 1/b, and a horizontal translation c units to the right. Find the equation for f(x) and g(x).[br][br][b]Question 5: [/b]Consider the equation h(x)=[math]\left(3\left(x-4\right)\right)^2[/math]. Write the two transformations required to transform f(x)= 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]