Stitz-Zeager_College_Algebra_e-book

# 4 use your graph in 1 to graph mx x 3 2 1 graph f

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: p 2 units’. Notice that the graph retains the same basic shape as before, it is just 2 units above its original location. In other words, we connect the four points we moved in the same manner in which they were connected before. We have the results side-by-side below. 1.8 Transformations 85 y y (5, 7) 7 7 6 6 (5, 5) (2, 5) 5 5 (4, 5) 4 4 (2, 3) (0, 3) 3 (4, 3) 2 2 (0, 1) 1 1 2 3 4 5 x shift up 2 units 1 2 3 4 5 x −− − − − −→ −−−−−− y = f (x) add 2 to each y -coordinate y = g (x) = f (x) + 2 You’ll note that the domain of f and the domain of g are the same, namely [0, 5], but that the range of f is [1, 5] while the range of g is [3, 7]. In general, shifting a function vertically like this will leave the domain unchanged, but could very well aﬀect the range. You can easily imagine what would happen if we wanted to graph the function j (x) = f (x) − 2. Instead of adding 2 to each of the y -coordinates on the graph of f , we’d be subtracting 2. Geometrically, we would be moving the graph down 2 units. We leave i...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online