In Exercises 81–86 , determine a rational function that meets the given conditions, and sketch its graph. The function g has vertical asymptotes at x = − 2 and x = 0 , a horizontal asymptote at y = − 3 , and g ( 1 ) = 4 .
In Exercises 81–86 , determine a rational function that meets the given conditions, and sketch its graph. The function g has vertical asymptotes at x = − 2 and x = 0 , a horizontal asymptote at y = − 3 , and g ( 1 ) = 4 .
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
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'
For Exercises 103–104, given y = f(x),
remainder
a. Divide the numerator by the denominator to write f(x) in the form f(x) = quotient +
divisor
b. Use transformations of y
1
to graph the function.
2x + 7
5х + 11
103. f(x)
104. f(x)
x + 3
x + 2
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