Transformations of Functions and Graphs

The video tutorial guides students through graphing a transformed function. It begins with a test problem involving a semicircle function and explains how to identify the parent function. The tutorial then details the transformations applied, including horizontal stretching by a factor of three, vertical stretching by a factor of two, and translating the graph four units down. The instructor provides a step-by-step approach to sketching the transformed graph, emphasizing the importance of understanding each transformation's impact on the function. The lesson concludes with a final sketch and encourages students to practice for better accuracy.

What is the initial function given in the problem?

• y = √(25 - x^2) - 4

• y = 2√(25 - (x/3)^2) - 4

• y = √(25 - (x/3)^2) + 4

• y = 2√(25 - x^2) + 4

What is the parent function of the given transformed function?

• x^2 + y^2 = 5

• x^2 + y^2 = 25

• x^2 + y^2 = 50

• x^2 + y^2 = 10

What is the radius of the semicircle in the parent function?

• 5 units

• 10 units

• 15 units

• 20 units

What is the significance of the y-value being greater than or equal to 0 in the parent function?

• It indicates a semicircle

• It indicates a full circle

• It indicates a parabola

• It indicates a line

How is the function horizontally stretched?

• By a factor of 5

• By a factor of 3

• By a factor of 2

• By a factor of 4

What happens to the x-values during the horizontal stretch?

• They are divided by 2

• They are multiplied by 2

• They are divided by 3

• They are multiplied by 3

What is the purpose of comparing the base function with the transformed function?

• To determine the new center

• To find the new radius

• To calculate the new domain

• To make sketching easier

What is the effect of the horizontal stretch on the radius of the semicircle?

• It becomes 15

• It becomes 10

• It remains 5

• It becomes 20

What is the new x-value of the endpoint after the horizontal stretch?

• 20

• 15

• 10

• 5

What is the effect of the vertical stretch on the function?

• Each point is stretched vertically by a factor of 2

• Each point is stretched vertically by a factor of 3

• Each point is compressed vertically by a factor of 2

• Each point is compressed vertically by a factor of 3