SOLUTION: 7. Graph the following function using transformations. Find the vertical and horizontal asymptotes. State the domain and range. Submit your graph.
f(x)=1/(x-5)³+1
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-> SOLUTION: 7. Graph the following function using transformations. Find the vertical and horizontal asymptotes. State the domain and range. Submit your graph.
f(x)=1/(x-5)³+1
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Question 466391: 7. Graph the following function using transformations. Find the vertical and horizontal asymptotes. State the domain and range. Submit your graph.
f(x)=1/(x-5)³+1 Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! Graph the following function using transformations. Find the vertical and horizontal asymptotes. State the domain and range. Submit your graph.
f(x)=1/(x-5)³+1
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Horizontal Asymptote:
When the degree of the numerator is less than the degree of the denominator, as in this case, the horizontal asymptote is the x-axis or y=0.
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To find the vertical asymptote set the denominator=0, then solve for x.
(x-5)^3+1=0
(x-5)^3=-1
Take cube root of both sides
x-5=-1
x=5-1=4
Vertical asymptote: x=4
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Domain: (-∞, 4) U (4, ∞)
Range: (-∞, 0) U (0, ∞)
See the graph below as a visual check on the answer.
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y=1/((x-5)^3+1)
(