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Chapter 4: Q. 31 (page 225)

In Problems 31– 42, graph each rational function using transformations.
$F (x) = 2 + \frac{1}{x}$

Short Answer

Expert verified

The graph of the function $F (x) = 2 + \frac{1}{x}$ is:

Step by step solution

01

Step 1. Given

The function $F (x) = 2 + \frac{1}{x}$

To graph the function.

02

Step 2. Graph the parent function

Graph the basic function $y = \frac{1}{x}$

03

Step 3. Graph the function by shifting.

Replace $y = \frac{1}{x}$ by

$y = 2 + \frac{1}{x}$ by shifting vertically upward to $2$ unit.

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Most popular questions from this chapter

Find the domain of the rational function.

$H (x) = \frac{3 x^{2} + x}{x^{2} + 4}$

Find the real zeros off. Use the real zeros to factorf. $f (x) = 2 x^{4} + 17 x^{3} + 35 x^{2} - 9 x - 45$

In Problems 21–32, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros.

$f (x) = x^{5} - x^{4} + 2 x^{2} + 3$

Make up a polynomial function that has the following characteristics: crosses the $x$ -axis at $- 1$ and $4$ , touches the $x -$ axis at $0$ and $2$ , and is above the x-axis between $0$ and $2$ . Give your polynomial function to a fellow classmate and ask for a written critique

Find the domain of the rational function.

$G (x) = \frac{6}{(x + 3) (4 - x)}$

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