In Exercises 81–86 , determine a rational function that meets the given conditions, and sketch its graph. The function h has vertical asymptotes at x = − 1 2 and x = 1 2 , a horizontal asymptote at y = 0 , and h ( 0 ) = − 3 .
In Exercises 81–86 , determine a rational function that meets the given conditions, and sketch its graph. The function h has vertical asymptotes at x = − 1 2 and x = 1 2 , a horizontal asymptote at y = 0 , and h ( 0 ) = − 3 .
Solution Summary: The author calculates a rational function that has vertical asymptotes at x=-12, and horizontal
In Exercises 37–40, graph the function to see whether it appears to
have a continuous extension to the given point a. If it does, use Trace
and Zoom to find a good candidate for the extended function's value at
a. If the function does not appear to have a continuous extension, can it
be extended to be continuous from the right or left? If so, what do you
think the extended function's value should be?
37. f(x)
a = 1
5 cos 0
38. g(0)
а 3 п/2
40
27'
39. h(t) = (1 + 1)'", a = 0
40. k(x)
a = 0
1 – 2.*1'
In Exercises 1–6, find the domain and range of each function.1. ƒ(x) = 1 + x2 2. ƒ(x) = 1 - 2x3. F(x) = sqrt(5x + 10) 4. g(x) = sqrt(x2 - 3x)5. ƒ(t) = 4/3 - t6. G(t) = 2/t2 - 16
Find the natural domain and graph the functions in Exercises 15–20.15. ƒ(x) = 5 - 2x 16. ƒ(x) = 1 - 2x - x217. g(x) = sqrt( | x | ) 18. g(x) = sqrt(-x)19. F(t) = t/ | t | 20. G(t) = 1/ | t |
Precalculus Enhanced with Graphing Utilities (7th Edition)
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