Transformations of Reciprocal Functions

Front

What is a reciprocal function?

Back

A reciprocal function is a function of the form f(x) = 1/x, where x is not equal to zero.

Front

What are vertical asymptotes?

Back

Vertical asymptotes are lines x = a where a function approaches infinity or negative infinity as x approaches a.

Front

What are horizontal asymptotes?

Back

Horizontal asymptotes are lines y = b where a function approaches b as x approaches infinity or negative infinity.

Front

How do you find vertical asymptotes of a rational function?

Back

Set the denominator equal to zero and solve for x.

Front

How do you find horizontal asymptotes of a rational function?

Back

Compare the degrees of the numerator and denominator: If degree of numerator < degree of denominator, y = 0; if equal, y = leading coefficient of numerator/leading coefficient of denominator.

Front

What is the range of a reciprocal function?

Back

The range of a reciprocal function is all real numbers except for zero.

Front

What does it mean to shift a function vertically?

Back

Shifting a function vertically means adding or subtracting a constant from the function's output.

Front

What does it mean to shift a function horizontally?

Back

Shifting a function horizontally means adding or subtracting a constant from the function's input.

Front

What is a vertical stretch of a function?

Back

A vertical stretch occurs when the output of the function is multiplied by a factor greater than 1.

Front

What is a vertical compression of a function?

Back

A vertical compression occurs when the output of the function is multiplied by a factor between 0 and 1.