Transformations in Graphing Functions

The video tutorial explains how to use transformations to sketch graphs, focusing on vertical stretch, reflection, horizontal compression, phase shift, and vertical translation. It demonstrates using the mapping rule to graph a transformed cosine function, plotting points, and identifying patterns. The tutorial emphasizes avoiding straight lines when connecting points and concludes with determining the domain and range of the function.

What is the primary purpose of using transformations in graphing?

• To change the color of the graph

• To adjust the scale of the graph

• To sketch graphs more accurately

• To eliminate the need for graph paper

Which transformation is indicated by a negative 'a' value?

• Reflection in the x-axis

• Reflection in the y-axis

• Horizontal stretch

• Vertical stretch

What does a 'k' value of 2 signify in transformations?

• Vertical stretch by 2

• Horizontal stretch by 2

• Horizontal compression by 2

• Vertical compression by 2

How is the mapping rule applied to the x-values in this video?

• x plus k over d

• x times k minus d

• x minus k times d

• x over k plus d

What pattern is observed in the x-values after applying the mapping rule?

• Decreasing by 45

• Increasing by 30

• Increasing by 45

• Decreasing by 30

Why should the points not be connected in a straight line?

• Because the graph is a parabola

• Because the graph is a circle

• Because the graph is a smooth curve

• Because the graph is a zigzag

What is the domain of the transformed function for one period?

• From -2 to 4

• From 0 to 180

• From 60 to 240

• From 0 to 360

What is the range of the transformed function?

• From -3 to 3

• From 0 to 1

• From 1 to 3

• From -2 to 4

How can the maximum value of the function be determined?

• By adding the axis to the amplitude

• By dividing the axis by the amplitude

• By subtracting the axis from the amplitude

• By multiplying the axis by the amplitude

What does the negative sign in the amplitude indicate?

• A reflection

• A horizontal stretch

• A vertical stretch

• A phase shift