Mixed Transformations - Horizontal
Consider the two functions, f(x) and g(x), shown below, which will have two transformations: horizontal translation and horizontal stretch.
f(x) will be stretched first, followed by a translation.
g(x) will be translated first, followed by a stretch.
Play around with this, and then answer the questions below.
Question 1: Does the order of horizontal translations and horizontal stretches affect each other?
Question 2: 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?
Question 3: 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?
Question 4: 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).
Question 5: Consider the equation h(x)=. Write the two transformations required to transform f(x)= to h(x) if:
A: We do a stretch first;
B: We do a translation first.