Stitz-Zeager_College_Algebra_e-book

# Y y 4 2 2 2 4 2 1 1 1 1 1 1 0 0 4 3 2

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: ﬁrm the domain of g is [0, ∞) and ﬁnd the range of g to be [−1, ∞). 88 Relations and Functions y y (4, 2) 2 2 (1, 1) (4, 1) 1 1 (1, 0) (0, 0) 1 2 3 x 4 1 2 3 x 4 (0, −1) shift down 1 unit y = f (x) = √ −− − − − −→ −−−−−− x subtract 1 from each y -coordinate y = g ( x) = √ x−1 3. Solving x − 1 ≥ 0 gives x ≥ 1, so the domain of j is [1, ∞). To graph j , we note that j (x) = f (x − 1). In other words, we are subtracting 1 from the input of f . According to Theorem 1.3, this induces a shift to the right of the graph of f . We add 1 to the x-coordinates of the points on the graph of f and get the result below. The graph reaﬃrms the domain of j is [1, ∞) and tells us that the range is [0, ∞). y y (5, 2) (4, 2) 2 2 (2, 1) (1, 1) 1 1 (0, 0) 1 2 3 y = f (x) = 4 √ 5 x shift right 1 unit (1, 0) 2 3 −− − − − −→ −−−−−− x add 1 to each x-coordinate y = j (x) = 4 √ x 5 x−1 4. To ﬁnd the domain of m, we solve x + 3 ≥ 0 and get [−3, ∞). Comparing th...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online