Week 6

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Week Six

**1.**Find the domain of the function.

ANSWER:

What is the domain of g? ________

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

ANSWER:

___________ (Simplify your answer.)

**3.**For and find the following functions.

a.

b.

c.

d.

ANSWERS:

- __________(Simplify your answer.)
- _________ (Simplify your answer.)
- __________(Simplify your answer.)
- __________(Simplify your answer.)

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

ANSWERS:

- ___________(Simplify your answer.)
- ___________(Simplify your answer.)

**5.**The function is one-to-one.

Find an equation for the inverse function.

ANSWER:

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

ANSWERS:

Choose the correct answer below.

- -No
- -Yes

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

ANSWER:

Use a graphing tool to graph the function.

**8.**Find the domain of the following rational function.

ANSWER:

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

- The domain of H(x) is {x|x≠_______}. (Type the interger or a fraction. Use a comma to separate answers as needed.)
- 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.

ANSWER:

As x → , f(x) →________.

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

ANSWER:

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.)

- The vertical asymptote(s) is(are)________ and hole(s) corresponding to __________.
- 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.

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

ANSWER:

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

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

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

ANSWER:

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.

ANSWER:

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.

- The solution is ________. (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)
- 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.

ANSWER:

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.

- The solution set is ________.(Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)
- 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.

ANSWER:

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.

- The solution set is _________.(Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)
- The solution set is the empty set.

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