Transformations of Rational Functions

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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What is the parent function of rational functions?

Back

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How does the graph of a rational function behave as x approaches zero?

Back

As x approaches zero, the value of the rational function tends to infinity or negative infinity, depending on the direction from which x approaches zero.

Front

What does it mean to translate a function?

Back

To translate a function means to shift its graph horizontally and/or vertically without changing its shape.

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Back

Front

What is the effect of subtracting a constant from the input of a function?

Back

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Back

The parameter 'a' represents a vertical stretch or compression of the graph. If |a| > 1, the graph stretches; if 0 < |a| < 1, it compresses.

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Back

The parameter 'h' represents a horizontal shift of the graph. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.

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The parameter 'k' represents a vertical shift of the graph. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

How do you identify vertical asymptotes in a rational function?

Back

Vertical asymptotes occur where the denominator of the rational function equals zero, as the function approaches infinity.