Learn how to graph a rational expression with symmetry about the origin

The video tutorial covers the process of graphing a function by identifying vertical and horizontal asymptotes, checking for symmetry, and choosing points for graphing. The instructor explains how to solve for vertical asymptotes by setting the denominator to zero and discusses horizontal asymptotes by comparing the degrees of the numerator and denominator. Symmetry is checked by evaluating the function for negative inputs, and points are chosen to understand the graph's behavior around asymptotes. The session concludes with a sketch of the graph using symmetry and chosen points.

What is the first step in identifying vertical asymptotes?

• Set the numerator equal to zero and solve.

• Set the denominator equal to zero and solve.

• Find the degree of the numerator.

• Find the degree of the denominator.

How do you determine the horizontal asymptote when the degree of the numerator is less than the degree of the denominator?

• y = infinity

• y = 0

• y = x

• y = 1

What does it mean if a graph is symmetrical about the origin?

• It has no symmetry.

• It is identical on both sides of the y-axis.

• It is identical on both sides of the x-axis.

• It can be reflected over both the x and y axes.

When checking for symmetry, what function do you evaluate?

• F of x squared

• F of negative x

• F of x

• F of x cubed

What is recommended if you do not have a graphing calculator?

• Do not choose any points.

• Choose one point to the left of each asymptote.

• Choose two points to the left and right of each asymptote.

• Choose three points anywhere on the graph.

What is the purpose of choosing points when graphing?

• To determine the color of the graph.

• To find the exact value of the asymptotes.

• To calculate the area under the graph.

• To understand the shape and direction of the graph.

How do asymptotes help in understanding the domain of a graph?

• They show where the graph is continuous.

• They indicate values that are part of the graph.

• They determine the range of the graph.

• They represent values that make the graph discontinuous.