x2 - 81Follow the steps for graphing a rational function to graph the function H(x) =x* - 16If needed, first write the given function as a single rational expression. Then, factor the numerator and denominator of H(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.А. Нx) 3(Do not simplify.)B. H(x) cannot be factored further.What is the domain of H(x)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.O A. {x|x2 } (Type an integer or a simplified fraction.)O B. {x)x+}(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)O C. {x\x<(Type an integer or a simplified fraction.)D. The domain is the set of all real numbers.Write H(x) in lowest terms. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.O A. H(x) =(Simplify your answer.)O B. H(x) is in lowest terms.Locate the intercept(s) of the graph. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.O A. The graph has y-interceptand x-intercept(s)(Simplify your answers. Type integers or fractions. Use a comma to separate answers as needed. Type each answer only once.)B. The graph has x-intercept(s)and no y-intercept.(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.)C. The graph has y-interceptand no x-intercept.(Simplify your answer. Type an integer or a fraction.) Determine the oblique asymptote(s), if one exists. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.O A. The function has one oblique asymptote,(Type an equation. Use integers or fractions for any numbers in the equation.)B. The function has two oblique asymptotes. The oblique asymptote with a negative slope is(Type equations. Use integers or fractions for any numbers in the equations.)and the oblique asymptote with a positive slope isOC. The function has no oblique asymptote.Determine the points, if any, at which the graph of H intersects the horizontal or oblique asymptote, if one exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.O A. The graph of H intersects the horizontal or oblique asymptote at infinitely many points.B. The graph of H intersects the horizontal or oblique asymptote at.(Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)C. There is no point at which the graph of H intersects the horizontal or oblique asymptote.D. There is no horizontal or oblique asymptote.Use the real zeros of the numerator and denominator of H to divide the x-axis into intervals. Determine where the graph of H is above or below the x-axis by choosing a number in each interval and evaluating H there. Select the correct choicebelow and fill in the answer box(es) to complete your choice.A. The graph of H is below the x-axis on the interval(s).(Type your answer in interval notation. Use a comma to separate answers as needed.)B. The graph of H is above the x-axis on the interval(s).(Type your answer in interval notation. Use a comma to separate answers as needed.)C. The graph of H is above the x-axis on the interval(s) and below the x-axis on the interval(s)(Type your answers in interval notation. Use a comma to separate answers as needed.)

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x² - 81 Follow the steps for graphing a rational function to graph the function H(x) = ** - 16 f needed, first write the given function as a single rational expression. Then, factor the numerator and denominator of H(x). Select the correct choice below and, necessary, fill in the answer box to complete your choice. O A. H(x) = (Do not simplify.) O B. H(x) cannot be factored further. What is the domain of H(x)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. {x)x2} (Type an integer or a simplified fraction.) O B. (xx +} (Type an integer or a simplified fraction. Use a comma separate answers as needed.) O C. {x)x<} (Type an integer or a simplified fraction.) O D. The domain is the set of all real numbers. Write H(x) in lowest terms. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. H(x) = (Simplify your answer.) O B. H(x) is in lowest terms.

x² - 81 Follow the steps for graphing a rational function to graph the function H(x) = ** - 16 f needed, first write the given function as a single rational expression. Then, factor the numerator and denominator of H(x). Select the correct choice below and, necessary, fill in the answer box to complete your choice. O A. H(x) = (Do not simplify.) O B. H(x) cannot be factored further. What is the domain of H(x)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. {x)x2} (Type an integer or a simplified fraction.) O B. (xx +} (Type an integer or a simplified fraction. Use a comma separate answers as needed.) O C. {x)x<} (Type an integer or a simplified fraction.) O D. The domain is the set of all real numbers. Write H(x) in lowest terms. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. H(x) = (Simplify your answer.) O B. H(x) is in lowest terms.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

x2 - 81
Follow the steps for graphing a rational function to graph the function H(x) =
x* - 16
If needed, first write the given function as a single rational expression. Then, factor the numerator and denominator of H(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
А. Нx) 3
(Do not simplify.)
B. H(x) cannot be factored further.
What is the domain of H(x)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. {x|x2 } (Type an integer or a simplified fraction.)
O B. {x)x+}
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
O C. {x\x<
(Type an integer or a simplified fraction.)
D. The domain is the set of all real numbers.
Write H(x) in lowest terms. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. H(x) =
(Simplify your answer.)
O B. H(x) is in lowest terms.
Locate the intercept(s) of the graph. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
O A. The graph has y-intercept
and x-intercept(s)
(Simplify your answers. Type integers or fractions. Use a comma to separate answers as needed. Type each answer only once.)
B. The graph has x-intercept(s)
and no y-intercept.
(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.)
C. The graph has y-intercept
and no x-intercept.
(Simplify your answer. Type an integer or a fraction.)

Determine the oblique asymptote(s), if one exists. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
O A. The function has one oblique asymptote,
(Type an equation. Use integers or fractions for any numbers in the equation.)
B. The function has two oblique asymptotes. The oblique asymptote with a negative slope is
(Type equations. Use integers or fractions for any numbers in the equations.)
and the oblique asymptote with a positive slope is
OC. The function has no oblique asymptote.
Determine the points, if any, at which the graph of H intersects the horizontal or oblique asymptote, if one exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The graph of H intersects the horizontal or oblique asymptote at infinitely many points.
B. The graph of H intersects the horizontal or oblique asymptote at.
(Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)
C. There is no point at which the graph of H intersects the horizontal or oblique asymptote.
D. There is no horizontal or oblique asymptote.
Use the real zeros of the numerator and denominator of H to divide the x-axis into intervals. Determine where the graph of H is above or below the x-axis by choosing a number in each interval and evaluating H there. Select the correct choice
below and fill in the answer box(es) to complete your choice.
A. The graph of H is below the x-axis on the interval(s).
(Type your answer in interval notation. Use a comma to separate answers as needed.)
B. The graph of H is above the x-axis on the interval(s).
(Type your answer in interval notation. Use a comma to separate answers as needed.)
C. The graph of H is above the x-axis on the interval(s) and below the x-axis on the interval(s)
(Type your answers in interval notation. Use a comma to separate answers as needed.)

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