Googleクラスルーム
GeoGebraGeoGebra Classroom

Mixed Transformations - Vertical

Consider the two functions, f(x) and g(x), shown below, which will have two transformations: vertical translation and vertical 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 vertical translations and vertical stretches affect each other? Question 2: 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? Question 3: Consider a vertical reflection, and a vertical translation up 2 units. Find the equation for f(x) and g(x). Are they equal? Question 4: 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). 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.