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

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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...
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