Exploring Horizontal and Vertical Stretches in Function Graphs

This video tutorial introduces function transformations, focusing on vertical and horizontal stretches and compressions. It explains how the values of 'A' and 'B' affect the graph of a function, using examples like y = A * f(x) and y = f(Bx). The video demonstrates these transformations through T tables and graph comparisons, highlighting the effects of different values of 'A' and 'B'. It also includes animations to visualize these changes and provides practical examples to help understand the concepts better.

What does a value of 'A' greater than 1 do to the graph of f(x)?

• Compresses the graph vertically

• Stretches the graph vertically

• Compresses the graph horizontally

• Stretches the graph horizontally

What effect does a value of 'A' between 0 and 1 have on the graph of f(x)?

• Vertical stretch

• Horizontal compression

• Vertical compression

• Horizontal stretch

How do you find the y-coordinates of a transformed function with the same x-coordinates?

• Divide each y-coordinate by 'A'

• Leave the y-coordinates the same

• Multiply each x-coordinate by 'A'

• Multiply each y-coordinate by 'A'

What does a value of 'B' greater than 1 do to the graph of f(x)?

• Stretches the graph vertically

• Compresses the graph horizontally

• Stretches the graph horizontally

• Compresses the graph vertically

What effect does a value of 'B' between 0 and 1 have on the graph of f(x)?

• Horizontal stretch

• Vertical compression

• Horizontal compression

• Vertical stretch

What is the parent function of f(x) = 3 |x|?

• f(x) = sqrt(x)

• f(x) = x^3

• f(x) = x^2

• f(x) = |x|

How is the graph of f(x) = 3 |x| transformed from its parent function?

• Horizontal compression by a factor of 3

• Vertical stretch by a factor of 3

• Vertical compression by a factor of 3

• Horizontal stretch by a factor of 3

What is the parent function of f(x) = sqrt(2x)?

• f(x) = x^2

• f(x) = |x|

• f(x) = sqrt(x)

• f(x) = 2x

How is the graph of f(x) = sqrt(2x) transformed from its parent function?

• Horizontal stretch by a factor of 2

• Vertical compression by a factor of 2

• Vertical stretch by a factor of 2

• Horizontal compression by a factor of 2

What transformation does the graph of f(x) = sqrt(2x) undergo?

• Vertical compression

• Vertical stretch

• Horizontal compression

• Horizontal stretch