Exploring Horizontal Shrink and Stretch Transformations

This video tutorial explains horizontal shrinks and stretches of linear functions. It covers how these transformations are applied by multiplying the x-coordinate by a number 'a'. A value of 'a' greater than one results in a shrink, while a value between zero and one results in a stretch. The video provides examples and compares these transformations to vertical ones, highlighting their similarities and differences.

What is the purpose of performing horizontal shrinks and stretches on linear functions?

• To make the function non-linear

• To change the slope of the function

• To transform the parent function into different linear functions

• To change the y-intercept of the function

What happens when you multiply the x-coordinate by a number greater than one?

• The graph stretches horizontally

• The graph remains unchanged

• The graph shrinks horizontally

• The graph reflects over the y-axis

If the number 'a' used for transformation is between zero and one, what type of transformation occurs?

• Horizontal stretch

• Vertical shrink

• Horizontal shrink

• Vertical stretch

In the example of a horizontal shrink, what is the transformed function when f(x) = x + 2 and a = 2?

• h(x) = 2x - 2

• h(x) = x + 4

• h(x) = x/2 + 2

• h(x) = 2x + 2

What is the y-value of the point (2, 4) after a horizontal shrink with a = 2?

• 2

• 4

• 6

• 8

In the example of a horizontal stretch, what is the transformed function when f(x) = x + 2 and a = 0.5?

• h(x) = 0.5x + 2

• h(x) = 2x + 2

• h(x) = x + 4

• h(x) = x/2 + 2

What is the y-value of the point (2, 4) after a horizontal stretch with a = 0.5?

• 3

• 4

• 2

• 5

Why does the intercept remain unchanged during horizontal stretches and shrinks?

• Because the slope remains constant

• Because the x-intercept is always zero

• Because zero times any number is zero

• Because the y-intercept is always zero

How is a vertical shrink related to a horizontal stretch?

• They are opposite transformations

• They are equivalent transformations

• They have no relation

• They both change the y-intercept

What happens if you use a negative value for 'a' in the transformation?

• The graph stretches horizontally

• The graph shrinks horizontally

• The graph remains unchanged

• The graph reflects over the y-axis