Transformations - Video Tutorials & Practice Problems
Introduction to Transformations
Reflections of Functions
Example 1
Written below (green dotted curve) is a graph of the function f(x)=x−2. If g(x) (blue solid curve) is a reflection of f(x) about the y-axis what is the equation for g(x)?
g(x)=−x−2
g(x)=−x−2
g(x)=x−2
g(x)=x−2
Shifting A Functions
The green dotted line in the graph below represents the function f(x). The blue solid line represents the function g(x), which is the function f(x) after it has gone through a shift transformation. Find the equation for g(x).
g(x)=f(x−2)+3
g(x)=f(x−2)−3
g(x)=f(x+2)−3
g(x)=f(x)−3
Graphs of Shifted and Reflected Functions
Example 2
Stretches and Shrinks of Functions
Example 3
Domain and Range of Function Transformations
The green dotted curve below is a graph of the function f(x). Find the domain and range of g(x) (the blue solid curve), which is a transformation of f(x).
Dom: [1,4] , Ran: [−5,−1]
Dom: [1,5] , Ran: [−5,1]
Dom: [−1,3] , Ran: [−2,4]
Dom: [−2,3] , Ran: [2,4]