Simplify the expression $$\frac{x-3}{x}$$ .

The simplified expression is $$\frac{x-3}{x}$$ .

What is the horizontal asymptote of the function $$y = \frac{2x^2 + 3}{4x^2 - 5}$$ ?

The horizontal asymptote is y = $$\frac{2}{4} = \frac{1}{2}$$ .

Simplify the expression $$\frac{x+9}{x-9}$$ .

The simplified expression is $$\frac{x+9}{x-9}$$ .

What is the horizontal asymptote of the function $$y = \frac{5x^3 + 2}{3x^3 - 1}$$ ?

The horizontal asymptote is y = $$\frac{5}{3}$$ .

Identify the horizontal asymptote for the function $$y = \frac{1}{x}$$ .

The horizontal asymptote is y = 0.

What is the equation of the horizontal asymptote for the function $$y = \frac{7}{x} + 1$$ ?

The horizontal asymptote is y = 1.

Simplify the expression $$\frac{1}{(x-9)}$$ .

The simplified expression is $$\frac{1}{(x-9)}$$ .

What is the horizontal asymptote of the function $$y = \frac{x^2 + 1}{x^2 + 2}$$ ?

The horizontal asymptote is y = 1.

What is the significance of horizontal asymptotes in graphing functions?

Horizontal asymptotes indicate the behavior of a function as x approaches infinity or negative infinity, helping to understand the end behavior of the graph.

Simplify the expression $$\frac{x^2 - 1}{x^2 - 4}$$ .

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

Horizontal/Vertical Asymptotes and simplifying Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as the input (x) approaches positive or negative infinity.

2.

FLASHCARD QUESTION

Front

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

Back

3.

FLASHCARD QUESTION

Front

Back

The horizontal asymptote is y = 2.

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What does it mean to simplify an algebraic fraction?

Back

To simplify an algebraic fraction means to reduce it to its simplest form by canceling common factors in the numerator and denominator.

7.

FLASHCARD QUESTION

Front

Back

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