Understanding Graphs and Transformations

The video tutorial introduces rectangular hyperbolas, focusing on the graph of y = 1/x. It explains the concept of asymptotes and their importance in graphing. The tutorial covers how transformations like dilation, reflection, and translation affect the position of asymptotes. Several examples demonstrate graphing hyperbolas with different transformations, and the video concludes with complex graphing scenarios and algebraic simplification techniques.

What is a rectangular hyperbola?

• A graph with two asymptotes at right angles

• A type of ellipse

• A circle with a radius of one

• A line that never crosses the x-axis

What happens to the value of y as x increases in the graph of y = 1/x?

• y becomes negative

• y becomes smaller

• y becomes larger

• y remains constant

What is an asymptote?

• A point where the graph crosses the axis

• A line that a graph approaches but never touches

• A point of maximum curvature

• A curve that intersects the graph

Which transformation involves multiplying all y-values by a number?

• Rotation

• Translation

• Reflection

• Dilation

In the graph of y = -3/x, what does the negative sign indicate?

• A translation upwards

• A dilation by a factor of three

• A reflection in the x-axis

• A shift to the right

How can you rewrite 5x + 3 over x + 1 to show its equivalence to another form?

• By dividing by a constant

• By factoring out common terms

• By adding a constant

• By multiplying by x