How does the function $$f(x) = \frac{1}{x} + 3$$ transform the graph of $$f(x) = \frac{1}{x}$$ ?

The graph of $$f(x) = \frac{1}{x} + 3$$ is a vertical translation of the graph of $$f(x) = \frac{1}{x}$$ , moving it 3 units up.

What is the range of the function $$y = \frac{1}{x}$$ ?

The range of $$y = \frac{1}{x}$$ is all real numbers except 0, or $$y \ne 0$$ .

What is the domain of the function $$y = \frac{1}{x}$$ ?

The domain of $$y = \frac{1}{x}$$ is all real numbers except 0, or $$x \ne 0$$ .

Does the equation $$y = \frac{10}{x}$$ show an inverse variation?

Yes, the equation $$y = \frac{10}{x}$$ shows inverse variation.

What is a vertical asymptote?

A vertical asymptote is a vertical line $$x = a$$ where a function approaches infinity or negative infinity.

What is a horizontal asymptote?

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

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

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

What is the significance of the x-intercept in a graph?

The x-intercept is the point where the graph crosses the x-axis, indicating where the function equals zero.

What is the significance of the y-intercept in a graph?

The y-intercept is the point where the graph crosses the y-axis, indicating the value of the function when $$x = 0$$ .

How does the transformation $$f(x) = \frac{1}{x-4} + 3$$ affect the graph of $$f(x) = \frac{1}{x}$$ ?

The graph of $$f(x) = \frac{1}{x-4} + 3$$ is shifted 4 units to the right and 3 units up from the graph of $$f(x) = \frac{1}{x}$$ .

Graphing Rational Functions Flashcard Review Flashcards

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1.

FLASHCARD QUESTION

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

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