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Chapter 1: Q. 22 (page 149)

Find the equation of a rational function that could have the graph shown. Take into account roots, holes, and vertical and horizontal asymptotes when constructing your function.

Short Answer

Expert verified

Ans: $(x) = \{\begin{cases} \frac{x}{1 - x^{2}} : - 1 < x < 1 \\ \frac{2 x}{1 - x^{2}} + 2 : x > 1 \\ \frac{2 x}{1 - x^{2}} + 2 : x < - 1 \end{cases}$

Step by step solution

01

Step 1. Given information.

given,

the rational function that could have the graph given in the question.

02

Step 2. The function would be

$(x) = \{\begin{cases} \frac{x}{1 - x^{2}} : - 1 < x < 1 \\ \frac{2 x}{1 - x^{2}} + 2 : x > 1 \\ \frac{2 x}{1 - x^{2}} + 2 : x < - 1 \end{cases}$

03

Step 3. Now the graph of the function is given below

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Most popular questions from this chapter

Calculate each of the limits:

$\lim_{x \to 0} \frac{1}{s e c^{- 1} x}$ .

In Exercises 39–44, use Theorem 1.16 and left and right limits to determine whether each function f is continuous at its break point(s). For each discontinuity of f, describe the type of discontinuity and any one-sided discontinuity.

$f (x) = \{\begin{matrix} \sqrt{- x}, i f x < 0 \\ 2, i f x = 0 \\ \sqrt{x}, i f x > 0 \end{matrix} .$

For each limit statement , use algebra to find δ > 0 in terms of $ε$ > 0 so that if 0 < |x − c| < δ, then | f(x) − L| < $ε$ .

$\lim_{x \to 3} (x + 5) = 8$

Write each of the inequalities in interval notation:

$0 < | x - 2 | < 0.1$

For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.

$\lim_{x \to - 5} (3 x - 2) .$

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