Exploring Vertical and Horizontal Transformations in Functions

The video tutorial covers the concepts of stretching and compressing functions, focusing on horizontal and vertical transformations. It provides examples and explains how to apply these transformations using both notation and graphing methods. The tutorial demonstrates how horizontal stretching affects the slope of a function and how vertical stretching changes the y-coordinates, offering a comprehensive understanding of these mathematical transformations.

What is the primary focus of this video tutorial?

• Finding the roots of polynomials

• Graphing linear equations

• Stretching and compressing functions

• Solving quadratic equations

When horizontally stretching a function by a factor of two, what happens to the slope?

• It doubles

• It remains the same

• It halves

• It becomes negative

In horizontal stretching, which part of the function is affected?

• Neither X nor Y portions

• Both X and Y portions

• The X portion

• The Y portion

What is the new function G(x) when the original function f(x) = 3x - 2 is horizontally stretched by a factor of two?

• G(x) = 3x - 4

• G(x) = 3(1/2x) - 2

• G(x) = 3(2x) - 2

• G(x) = 3x - 2

What is the Y-intercept of the new function after horizontal stretching?

• 2

• 0

• -2

• -4

What happens to the slope when a function is vertically stretched by a factor of two?

• It becomes negative

• It doubles

• It remains the same

• It halves

In vertical stretching, which part of the function is affected?

• Both X and Y portions

• The Y portion

• Neither X nor Y portions

• The X portion

What is the new function G(x) when the original function f(x) = 3x - 2 is vertically stretched by a factor of two?

• G(x) = 6x - 2

• G(x) = 3x - 2

• G(x) = 3x - 4

• G(x) = 6x - 4

What is the Y-intercept of the new function after vertical stretching?

• 2

• -4

• -2

• 0

What is the slope of the new function after vertical stretching?

• 3

• 6

• 1.5

• 2