How do you find the y-intercept of the function $$f(x) = -\frac{4}{x-3}$$ ?

To find the y-intercept, substitute $$x = 0$$ into the function: $$f(0) = -\frac{4}{0-3} = \frac{4}{3}$$ .

Given the function $$f(x) = \frac{1}{x-2}$$ , what is the vertical asymptote?

The vertical asymptote is at $$x = 2$$ .

What is the x-intercept of a function?

The x-intercept of a function is the point where the graph intersects the x-axis, which occurs when $$f(x) = 0$$ .

How do you find the x-intercept of the function $$f(x) = -\frac{4}{x-3}$$ ?

Set the function equal to zero: $$-\frac{4}{x-3} = 0$$ . This gives no solution, indicating there is no x-intercept.

What is the significance of the degree of the numerator and denominator in a rational function?

The degree of the numerator and denominator helps determine the end behavior of the function and the presence of horizontal asymptotes.

What is a horizontal asymptote?

A horizontal asymptote is a horizontal line $$y = b$$ that the graph of a function approaches as $$x$$ approaches infinity or negative infinity.

How do you find horizontal asymptotes for rational functions?

Compare the degrees of the numerator and denominator: If the degree of the numerator is less, the horizontal asymptote is $$y = 0$$ ; if equal, $$y = \frac{a}{b}$$ where a and b are leading coefficients.

What happens to the graph of a rational function at a vertical asymptote?

As the function approaches the vertical asymptote, the graph will rise or fall towards infinity or negative infinity.

What is the relationship between holes and vertical asymptotes?

Holes indicate removable discontinuities, while vertical asymptotes indicate non-removable discontinuities in the graph of a rational function.

Given the function $$f(x) = \frac{1}{x^2 - 4}$$ , identify the vertical asymptotes.

The vertical asymptotes are at $$x = 2$$ and $$x = -2$$ , where the denominator equals zero.

Rational Function Graphs

Flashcard

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Mathematics

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9th - 12th Grade

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Practice Problem

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Hard

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FLASHCARD QUESTION

Front

What is a rational function?

Back

FLASHCARD QUESTION

Front

What is the y-intercept of a function?

Back

FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

What is a vertical asymptote?

Back

FLASHCARD QUESTION

Front

How do you determine vertical asymptotes of a rational function?

Back

FLASHCARD QUESTION

Front

What is a hole in a graph of a rational function?

Back

A hole occurs in the graph of a rational function at a point where both the numerator and denominator are zero, indicating a removable discontinuity.

FLASHCARD QUESTION

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