To find: all horizontal and vertical asymptotes of the function.
Vertical asymptote: x=2 .
Horizontal asymptote: y=0 .
Given information:
The function g(x)=4x−4x3−8 .
Calculation:
Graph of
g(x)=4x−4x3−8
Let y=g(x) .
Putting the value of x=0 then y=0.5 .
And x=1 , y=0
And x=2 , y=∞
Plot the graph:
By inspection of the graph, vertical asymptote is at x=2 and horizontal asymptote is at y=0 .
Algebraically, the vertical asymptote corresponds to the fact that x=2 is
excluded from the domain, as that would cause a division by zero.
To demonstrate the horizontal asymptote. Now, it's sufficient to say that, as x approaches infinity, the denominator becomes increasingly larger than the numerator, and the quotient of the division approaches zero.
Therefore, horizontal asymptote: y=0 and vertical asymptote: x=2 .
Chapter 1 Solutions
PRECALCULUS:...COMMON CORE ED.-W/ACCESS
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