Algebra II: Rational Expressions and Functions flashcards

Question 1

What is a rational expression?

Accepted Answer

p/q, a quotient of polynomials p and q, with q ≠ 0

Question 2

What is a rational function?

Accepted Answer

A function R(x) = p(x)/q(x), with p and q polynomial functions and q(x) ≠ 0

Question 3

What is a complex rational expression?

Accepted Answer

A rational expression whose numerator, denominator or both contain a rational expression

Question 4

When is a rational expression simplified?

Accepted Answer

When its numerator and denominator share no common factor other than 1

Question 5

What is a proportion?

Accepted Answer

An equation stating that two ratios (rational expressions) are equal

Question 6

When are two figures similar?

Accepted Answer

When corresponding angles have equal measures and corresponding sides have the same ratio

Question 7

How is the proportion a/b = c/d read?

Accepted Answer

a is to b as c is to d

Question 8

Equivalent Fractions Property: a/b = ? (b ≠ 0, c ≠ 0)

Accepted Answer

(a·c)/(b·c)

Question 9

What is the opposite of a − b?

Accepted Answer

b − a

Question 10

Multiplying rational expressions: (p/q)·(r/s) = ? (q ≠ 0, s ≠ 0)

Accepted Answer

(pr)/(qs)

Question 11

Dividing rational expressions: (p/q) ÷ (r/s) = ? (q, r, s ≠ 0)

Accepted Answer

(p/q)·(s/r)

Question 12

Adding with a common denominator: p/r + q/r = ? (r ≠ 0)

Accepted Answer

(p + q)/r

Question 13

Subtracting with a common denominator: p/r − q/r = ? (r ≠ 0)

Accepted Answer

(p − q)/r

Question 14

The domain of a rational function excludes which values?

Accepted Answer

Values of x that make the denominator zero

Question 15

What equation describes y varying directly with x?

Accepted Answer

y = kx, with k ≠ 0

Question 16

What equation describes y varying inversely with x?

Accepted Answer

y = k/x, with k ≠ 0

Question 17

In direct or inverse variation, what is k called?

Accepted Answer

The constant of variation

Question 18

If triangles ABC and XYZ are similar, what is true of their corresponding sides?

Accepted Answer

They have the same ratio

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