Finding Asymptotes and Intercepts

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches. It can be vertical, horizontal, or oblique.

Front

How do you find the y-intercept of a function?

Back

To find the y-intercept, set x = 0 and solve for y.

Front

What is the x-intercept?

Back

The x-intercept is the point where the graph crosses the x-axis, found by setting y = 0 and solving for x.

Front

What does it mean to flip a graph over the x-axis?

Back

Flipping a graph over the x-axis means that for every point (x, y), the new point will be (x, -y).

Front

What does it mean to flip a graph over the y-axis?

Back

Flipping a graph over the y-axis means that for every point (x, y), the new point will be (-x, y).

Front

Back

The transformation is a flip over the x-axis.

Front

Back

The transformation is a right shift of 1 unit and an upward shift of 3 units.

Front

How do you find the x-intercept of a rational function?

Back

Replace the y-value with 0 or make the numerator equal to 0.

Front

What is a vertical asymptote?

Back

A vertical asymptote occurs where the function approaches infinity, typically where the denominator equals zero.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote indicates the behavior of a function as x approaches infinity or negative infinity.