Lesson 5E Just Act Rational Solidify Understanding

Ready

Use the given triangle to write the values of , , , , , and .

1.

A right triangle where angle C is 90 degrees with the corresponding side length of 15 centimeters. Angle A's corresponding side length is 12 centimeters and angle b's corresponding side length is 9 centimeters.

a.

b.

c.

d.

e.

f.

2.

A right triangle where angle C is 90 degrees with the corresponding side length of 3 centimeters. Angle A's corresponding side length is 1 centimeter and angle b's corresponding side length is the square root of 2 centimeters.

a.

b.

c.

d.

e.

f.

3.

A right triangle where angle C is 90 degrees with the corresponding side length of 7 times the square root of 2 meters. Angle A and B's corresponding side lengths are 7 meters.

a.

b.

c.

d.

e.

f.

4.

A right triangle where angle C is 90 degrees with the corresponding side length of 26 inches. Angle A's corresponding side length is 10 inches and angle B's corresponding side length is 24 inches.

a.

b.

c.

d.

e.

f.

Set

5.

Angela performed the indicated operations on the following rational expressions. Only one of the three problems is correct. Determine which one she answered correctly. Then identify Angela’s errors in the two that are incorrect and correct them.

a.

Is this problem correct? If not, correct Angela’s work.

b.

Is this problem correct? If not, correct Angela’s work.

c.

Is this problem correct? If not, correct Angela’s work.

Rewrite each expression.

6.

7.

8.

9.

10.

11.

12.

Rational numbers and rational expressions are comparable because they have similar features. Complete the table by writing the comparable situation for each statement written.

Rational Numbers

Rational Expressions

Whole numbers are rational numbers with a denominator of .

Rational expressions are undefined when the denominator is equal to .

When you add, subtract, multiply, or divide two rational numbers, the result is also a rational number.

Rational fractions are classified as proper fractions when the numeric value of the numerator is smaller than the denominator.

Go

Identify the values of for which the function is undefined, if any.

13.

14.

15.

16.

Use for problems 17–21.

17.

Describe the end behavior of .

18.

State the domain and range of .

19.

Identify the intercepts, if any.

20.

Write the equations of the asymptotes.

Horizontal:

Vertical:

21.

Graph . (Include any asymptotes with dotted lines.)

a blank 17 by 17 grid