# Math Paper Assignment | Homework Help Websites

Week 6

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Week Six

1.Find the domain of the function.

What is the domain of g? ________

2.Given  and , first find , ,  and . Then determine the domain for each function.

3.For  and  find the following functions.

a.

b.

c.

d.

4.Find and determine whether the pair of functions  are inverses of each other.

5.The function  is one-to-one.

Find an equation for  the inverse function.

6.Does the graph represent a function that has an inverse function?

• -No
• -Yes

7.Use the graph of f to draw the graph of its inverse function.

Use a graphing tool to graph the function.

8.Find the domain of the following rational function.

Select the correct choice below and, if necessary, fill in the answer box to complete the choice.

1. The domain of H(x) is {x|x≠_______}. (Type the interger or a fraction. Use a comma to separate answers as needed.)
2. The domain of H(x) has no restrictions.

9.Use the graph of the rational function to complete the following statement.

As x → , f(x) →________.

Asymptotes are shown as dashed lines.  The horizontal asymptote is y = -1.  The vertical asymptotes are x = -3 and x = 1.

As x → , f(x) →________.

1. 10. Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the rational function.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type the equation. Use commas to separate answers as needed.)

1. The vertical asymptote(s) is(are)________ and hole(s) corresponding to __________.
2. The vertical asymptote(s) is(are)________. There are no holes.

C.There are no vertical asymptotes but there is(are) hole(s) corresponding to ________.

D.There are no discontinuities.

1. Find the horizontal asymptote, if any, of the graph of the ration function.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

1. The horizontal asymptote is ___________. (Type the equation.)
2. There is no horizontal asymptote.

12.Follow the seven step strategy to graph the following rational function.

To graph the​ function, first determine the symmetry of the graph of . Choose the correct answer below.

• Y-axis symmetry
• Origin symmetry
• Neither y-axis nor origin symmetry

13.Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation.

Solve the inequality. What is the solution​ set? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

2. The solution set is the empty set.

14.Solve the rational inequality and graph the solution set on a real number line.  Express the solution set in interval notation.

Solve the inequality. What is the solution​ set? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

2. The solution set is the empty set.

15.Solve the rational inequality and graph the solution set on a real number line.  Express the solution set in interval notation.

Solve the inequality. What is the solution​ set? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

2. The solution set is the empty set.

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