Horizontal & Vertical Asymptotes, & Holes

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line that the graph of a function approaches as the function's value approaches infinity or negative infinity.

Front

What is a hole in a graph?

Back

A hole in a graph occurs at a point where a function is not defined due to a factor that cancels out in the function's expression.

Front

How do you find horizontal asymptotes for rational functions?

Back

To find horizontal asymptotes for rational functions, compare the degrees of the numerator and denominator. If the degree of the numerator is less, the asymptote is y=0. If they are equal, the asymptote is y=ratio of leading coefficients. If the numerator's degree is greater, there is no horizontal asymptote.

Front

What transformations occur when a function is shifted left or right?

Back

Shifting a function left or right involves adding or subtracting a value from the x-variable in the function's equation.

Front

What does it mean to reflect a function over the x-axis?

Back

Reflecting a function over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

What is a vertical stretch in a function?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

Front

How do you determine the transformations of the function f(x) = sqrt(x + 2)?

Back

The function f(x) = sqrt(x + 2) is transformed by shifting the parent function sqrt(x) left by 2 units.

Front

What is the effect of a negative sign in front of a function?

Back

A negative sign in front of a function reflects the graph over the x-axis.

Front

How do you find vertical asymptotes for rational functions?

Back

Vertical asymptotes occur at the values of x that make the denominator of a rational function equal to zero, provided that these values do not cancel with the numerator.