Exploring Simple Rational Functions Graphing Techniques

The video tutorial introduces reciprocal functions, focusing on asymptotes, including horizontal, vertical, and oblique types. It explains graphing simple rational functions using the parent graph y = 1/x, detailing the domain and range. The tutorial covers different forms of rational functions and provides a step-by-step example, including calculations for x and y intercepts and plotting points on a graph.

What is an asymptote?

• A line a graph touches at the origin.

• A line a graph approaches but never touches.

• A specific point on a graph.

• A curve that intersects the graph at various points.

What types of asymptotes are there?

• Horizontal, vertical, and oblique.

• Only oblique.

• Only horizontal and vertical.

• None, asymptotes do not exist.

For the function y = 1/x, what is the vertical asymptote?

• x = 1

• y = 0

• x = 0

• y = 1

For the function y = 1/x, what is the horizontal asymptote?

• y = 0

• x = 1

• y = 1

• x = 0

What is the domain of y = 1/x?

• Only positive real numbers

• All real numbers except x = 0

• Only negative real numbers

• All real numbers including x = 0

In the function y = a/(x-h) + k, what does 'h' represent?

• The horizontal asymptote

• The y-intercept of the graph

• The slope of the graph

• The x-coordinate of the vertical asymptote

In the function y = a/(x-h) + k, what does 'k' represent?

• The x-coordinate of the vertical asymptote

• The y-coordinate of the horizontal asymptote

• The slope of the graph

• The x-intercept of the graph

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

• By setting y = 0 and solving for x

• By setting x = 0 and solving for y

• By finding where the graph crosses the y-axis

• By calculating the slope between two points

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

• By calculating the slope between two points

• By finding where the graph crosses the x-axis

• By setting y = 0 and solving for x

• By setting x = 0 and solving for y

What is the significance of plotting at least four good points when graphing a rational function?

• To find the x and y intercepts

• To calculate the domain and range

• To accurately sketch the curve and its approach to the asymptotes

• To determine the slope of the graph