Mechanics, Transformations

Question

A) What are the domain and range of f(x)? [Note the arrow on the left side and the closed endpoint on the right side]

B) Label at least 5 key points on the graph. It helps to write them in a table. 

C) The original graph is transformed - it is shifted 2 units to the right and shifted 2 units up. Label where your 5 points have moved to, and draw a graph of the transformed function. What is the new formula for the transformed function in terms of f(x)? What are the new domain and range of the transformed graph? 

D) The original graph is transformed - there is a horizontal stretch by a factor of 2, and a vertical stretch by a factor of 2. Label where your 5 points have moved to, and draw a graph of the transformed function. What is the new formula for the transformed function in terms of f(x)? What are the new domain and range of the transformed graph? 

E) The original graph is transformed - there is a horizontal reflection over the y-axis and also a vertical reflection over the x-axis. Label where your 5 points have moved to, and draw a graph of the transformed function. What is the new formula for the transformed function in terms of f(x)? What are the new domain and range of the transformed graph?

Answer 1

domain is x<6

range is y>-2

(-2,0), (2,0), (6,0) are x intercepts

(0,2) is a local maximum

(4,-2) is a local minimum

move 2 right and up 2, then the points become

(0,2), (4,2), (8,2), (2,4), (6,0)

but two x intercepts disappear leaving only (6,0)

just add 2 to both the x and y coordinates

new domain is x>8, new range is y>0

new F(x) = f(x-2)+2