Graphing rational functions using 5 steps

The video tutorial covers the concept of asymptotes, including vertical and horizontal asymptotes, and how to find them using the degrees of the numerator and denominator. It also explains how to check for symmetry in functions and the importance of symmetry in graphing. The tutorial concludes with a demonstration of plotting points to graph a function, emphasizing the use of a calculator for accuracy.

What is the key characteristic of a vertical asymptote in a graph?

• The graph intersects the asymptote.

• The graph approaches but never touches the asymptote.

• The graph is symmetrical around the asymptote.

• The graph has a constant slope at the asymptote.

How do you determine the horizontal asymptote of a function?

• By comparing the leading coefficients of the numerator and denominator.

• By checking the symmetry of the function.

• By finding the roots of the function.

• By calculating the derivative of the function.

What does it indicate if f(-x) equals f(x) for a function?

• The function has no symmetry.

• The function is linear.

• The function is even.

• The function is odd.

Why is symmetry useful when plotting a graph?

• It helps in identifying the roots of the function.

• It allows you to find the slope easily.

• It simplifies the calculation of derivatives.

• It enables you to reflect points across the axis, reducing the number of calculations.

What should you do if a graph has no symmetry?

• Only plot points on one side of the asymptote.

• Use a calculator to find the exact shape of the graph.

• Ignore the asymptotes and plot randomly.

• Plot points on both sides of each asymptote.

When plotting points around an asymptote, what is a recommended approach?

• Plot points only on the right side of the asymptote.

• Plot only one point on each side of the asymptote.

• Plot two points on each side of the asymptote.

• Plot points only on the left side of the asymptote.

What is the purpose of using a calculator when plotting points for a graph?

• To calculate the derivative of the function.

• To assist in quickly finding values for plotted points.

• To verify the symmetry of the graph.

• To find the exact intersection points.