Graphing Rational Functions: Key Concepts and Techniques

The video tutorial covers translations of rational functions, focusing on transformations such as moving up, down, left, or right. It explains how to create a T-chart for graphing, plot points, and identify asymptotes. The concept of domain and range is introduced in a pre-calculus context. The tutorial also discusses transformations, reflections, and concludes with a homework assignment.

What type of transformations are involved in translations of rational functions?

• Shearing and compressing

• Shifting up/down or left/right

• Reflecting and stretching

• Scaling and rotating

What happens to a function when a minus sign is added at the end?

• It shifts up one unit

• It shifts down one unit

• It shifts left one unit

• It shifts right one unit

Why can't you have zero in the denominator of a rational function?

• It makes the function undefined

• It makes the function negative

• It makes the function infinite

• It makes the function zero

When plotting points for a rational function, why is it important to consider the asymptotes?

• To determine the range

• To make the graph symmetrical

• To avoid undefined points

• To ensure the graph is centered

What is the asymptote for the function given in the video?

• x = 0

• x = -1

• x = -2

• x = 1

How do you write the domain of a function that does not exist at x = -2?

• x = -2

• x ≠ -2

• x < -2

• x > -2

What is the range of the function if the asymptote is y = -1?

• y ≠ -1

• y = -1

• y > -1

• y < -1

What is the first transformation applied to the function in the video?

• Vertical stretch

• Vertical translation

• Horizontal translation

• Reflection over the x-axis

How many units is the function translated vertically?

• One unit up

• Two units up

• One unit down

• Two units down

What is the horizontal translation applied to the function?

• Two units to the right

• One unit to the left

• Two units to the left

• One unit to the right