Advanced Algebra Rational Numbers

What are the Vertical Asymptote(s)? Choose all that apply.

• x= -4

• x= 4

• x= 5

• x= -5

Which statements are true for the given rational function. Select all that apply.

• The domain is all real numbers except -2 AND 6.

• There is a removable discontinuity at x=6

• The vertical asymptote is x = -2

• The x and y intercepts are at the origin.

• The domain is all real numbers except -2.

What is the domain?

• (−∞,2)U(2,∞)

• (−∞,∞)

• (−∞,−2)U(2,∞)

• (−∞,−2)U(−2,2)U(2,∞)

• (1)

• (2)

• (3)

• (4)

Which statement is true?

• The product and sum of 4/9 and (square root of)17 are both irrational.

• The product and sum of 4/9 and (square root of)17 are both rational.

• The product of 4/9 and (square root of)17 is irrational, while the sum of 4/9 and (square root of)17 is rational.

• The product of 4/9 and (square root of)17 is rational, while the sum of 4/9 and (square root of)17 is irrational.

Is the result rational or irrational? Explain.

• Rational; The sum of two rationals is always rational.

• Irrational; The sum of a rational and an irrational is always irrational.

• Rational; The product of two rationals is always rational.

• Irrational; The product of a nonzero rational and an irrational is always irrational.

Let x be a nonzero rational number and y be an irrational number. Which of these expressions MUST be a rational number?

• y + 0

• x + x

• x + y

• y + y

Identify each statement as always, sometimes, or never true.

• Always

• Sometimes

• Never True

Jacinta says that the product of a rational number and an irrational number is always irrational. Explain her error.

What is the vertical asymptote?

Mathematical Equivalence

ON