Algebra 2 Unit 4 Review

Front

What is the domain of the rational function f(x) = \frac{x}{x^2 - 25}?

Back

The domain is all real numbers, x ≠ ±5.

Front

What is the domain for the function f(x) = \frac{2x - 1}{3x + 6}?

Back

The domain is all real numbers, x cannot equal -2.

Front

How do you solve the equation \frac{-2}{x-1} = \frac{x-8}{x+1} by cross multiplying?

Back

Cross multiply to get -2(x + 1) = (x - 8)(x - 1).

Front

What is the result of multiplying the rational expression \frac{a}{b} \cdot \frac{c}{d}?

Back

The result is \frac{ac}{bd}.

Front

What is the simplified form of \frac{4 - x^2}{x^2 - x - 2}?

Back

The simplified form is -\frac{(x + 2)}{(x + 1)}.

Front

What does it mean for a function to be undefined?

Back

A function is undefined at points where the denominator equals zero.

Front

What is the process of finding the least common denominator (LCD) for rational expressions?

Back

The LCD is the smallest expression that can be used to eliminate the denominators in a set of fractions.

Front

How do you determine if a rational function has vertical asymptotes?

Back

Vertical asymptotes occur at values of x that make the denominator zero, provided the numerator is not also zero at those points.

Front

What is the difference between a rational function and a polynomial function?

Back

A rational function is the ratio of two polynomials, while a polynomial function is just a single polynomial.

Front

What is the significance of the x-intercept in a rational function?

Back

The x-intercept is the value of x where the function equals zero, found by setting the numerator equal to zero.