Stitz-Zeager_College_Algebra_e-book

3 choose a test value in each of the intervals

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Unformatted text preview: the graphical observation. x 0.9 0.99 0.999 0.9999 h(x) (x, h(x)) ≈ 0.4210 ≈ (0.9, 0.4210) ≈ 0.4925 ≈ (0.99, 0.4925) ≈ 0.4992 ≈ (0.999, 0.4992) ≈ 0.4999 ≈ (0.9999, 0.4999) x 1.1 1.01 1.001 1.0001 h(x) (x, h(x)) ≈ 0.5714 ≈ (1.1, 0.5714) ≈ 0.5075 ≈ (1.01, 0.5075) ≈ 0.5007 ≈ (1.001, 0.5007) ≈ 0.5001 ≈ (1.0001, 0.5001) We see that as x → 1− , h(x) → 0.5− and as x → 1+ , h(x) → 0.5+ . In other words, the points on the graph of y = h(x) are approaching (1, 0.5), but since x = 1 is not in the domain of h, it would be inaccurate to fill in a point at (1, 0.5). As we’ve done in past sections when something like this occurs,4 we put an open circle (also called a ‘hole’ in this case5 ) at (1, 0.5). Below is a detailed graph of y = h(x), with the vertical and horizontal asymptotes as dashed lines. y 8 7 6 5 4 3 1 −4 −3 −2 1 2 3 4 x −1 −2 −3 −4 −5 −6 4 For instance, graphing piecewise defined functions in Section 1.7. Stay tuned. In Calculus, we will see how these ‘holes...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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