Example 173 analytically determine if the following

Unformatted text preview: sing fashion to get the graph below on the right. y x −3 −2 −1 0 1 2 3 4 f (x) (x, f (x)) 6 (−3, 6) 0 (−2, 0) −4 (−1, −4) −6 (0, −6) −6 (1, −6) −4 (2, −4) 0 (3, 0) 6 (4, 6) 7 6 5 4 3 2 1 −3 −2 −1 −1 −2 −3 −4 −5 −6 1 2 3 4 x 1.7 Graphs of Functions 65 Graphing piecewise-defined functions is a bit more of a challenge. Example 1.7.2. Graph: f (x) = 4 − x2 if x < 1 x − 3, if x ≥ 1 Solution. We proceed as before: finding intercepts, testing for symmetry and then plotting additional points as needed. To find the x-intercepts, as before, we set f (x) = 0. The twist is that we have two formulas for f (x). For x < 1, we use the formula f (x) = 4 − x2 . Setting f (x) = 0 gives 0 = 4 − x2 , so that x = ±2. However, of these two answers, only x = −2 fits in the domain x < 1 for this piece. This means the only x-intercept for the x < 1 region of the x-axis is (−2, 0). For x ≥ 1, f (x) = x − 3. Setting f (x) = 0 gives 0 = x − 3, or x = 3. Since x = 3 satisfies the inequality x ≥ 1, we get (3, 0) as another x-intercept. Next...
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