8.4-8.6 Unit 8 Review Flashcardizz

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line that a graph approaches but never touches or crosses. It occurs where a function's value becomes infinite.

Front

How do you find the vertical asymptote of a rational function?

Back

To find the vertical asymptote, set the denominator of the rational function equal to zero and solve for x.

Front

What is the equation of the vertical asymptote for the function \( f(x) = \frac{1}{x+3} \)?

Back

The vertical asymptote is \( x = -3 \).

Front

What are domain restrictions in a function?

Back

Domain restrictions are values that cannot be included in the domain of a function, often due to division by zero or square roots of negative numbers.

Front

If a function has a vertical asymptote at \( x = -3 \), what are the domain restrictions?

Back

The domain restriction is \( x \neq -3 \).

Front

Simplify the expression \( \frac{x^2 + 11x + 24}{x^2 + 4x - 32} \).

Back

The simplified form is \( \frac{x + 3}{x - 4} \).

Front

What is the process to simplify a complex fraction?

Back

To simplify a complex fraction, multiply the numerator and denominator by the least common denominator (LCD) of the fractions involved.

Front

Simplify the complex fraction \( \frac{\frac{2x-1}{x}}{\frac{2}{x}+3} \).

Back

The simplified form is \( \frac{2x-1}{2+3x} \).

Front

What does it mean for a function to be undefined?

Back

A function is undefined at points where the denominator is zero or where the function does not have a real value.

Front

What is the significance of horizontal asymptotes?

Back

Horizontal asymptotes indicate the behavior of a function as x approaches infinity or negative infinity.