Graphing Rational Functions (day 1)

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as the input approaches a. It indicates values that the function cannot take.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b that a function approaches as x approaches infinity or negative infinity. It indicates the behavior of the function at extreme values of x.

Front

How do you find vertical asymptotes of a rational function?

Back

Vertical asymptotes can be found by setting the denominator of the rational function equal to zero and solving for x.

Front

How do you find horizontal asymptotes of a rational function?

Back

Horizontal asymptotes can be determined by comparing the degrees of the numerator and denominator. If the degree of the numerator is less, y = 0; if equal, y = leading coefficient ratio; if greater, no horizontal asymptote.

Front

What is the parent function of rational functions?

Back

The parent function of rational functions is f(x) = 1/x.

Front

What does it mean to translate a function?

Back

Translating a function means shifting it horizontally or vertically without changing its shape.

Front

What is a reflection in graphing?

Back

A reflection in graphing occurs when a function is flipped over a specific axis, such as the x-axis or y-axis.

Front

What is the effect of a vertical shift on a function?

Back

A vertical shift moves the graph of the function up or down. For example, g(x) = f(x) + k shifts the graph up by k units if k > 0 and down if k < 0.

Front

What is the effect of a horizontal shift on a function?

Back

A horizontal shift moves the graph of the function left or right. For example, g(x) = f(x - h) shifts the graph right by h units if h > 0 and left if h < 0.

Front

What is the domain of a rational function?

Back

The domain of a rational function is all real numbers except where the denominator equals zero.