Transforming Linear Functions: Vertical and Horizontal Changes

This video tutorial covers transforming linear functions, focusing on the effects of multiplying the output and input. It includes examples demonstrating vertical and horizontal transformations, and concludes with a practice activity for identifying these transformations.

What is the primary focus of this lesson?

• Understanding quadratic functions

• Transforming linear functions

• Solving linear equations

• Graphing quadratic equations

What does multiplying the output of a linear function by a constant do to the graph?

• Stretches or compresses it vertically

• Shifts it vertically

• Shifts it horizontally

• Reflects it over the x-axis

In the example G(x) = 4 * f(x), what is the effect on the graph?

• Vertical stretch

• Horizontal compression

• Vertical compression

• Horizontal shift

What happens to the y-intercept when the output of a linear function is multiplied by a constant?

• It is shifted horizontally

• It remains the same

• It is scaled by the same factor

• It is reflected over the y-axis

If k is greater than 1, what type of transformation occurs when multiplying the output of a function by k?

• Horizontal stretch

• Vertical stretch

• Horizontal compression

• Vertical compression

How does multiplying the input of a linear function by a constant affect the graph?

• Stretches or compresses it horizontally

• Shifts it vertically

• Reflects it over the y-axis

• Shifts it horizontally

In the example G(x) = f(3x), what is the effect on the graph?

• Vertical compression

• Vertical stretch

• Horizontal stretch

• Horizontal compression

What remains unchanged when the input of a linear function is multiplied by a constant?

• Slope

• Y-intercept

• X-intercept

• Both intercepts

If k is between 0 and 1, what type of transformation occurs when multiplying the input of a function by k?

• Horizontal compression

• Vertical compression

• Vertical stretch

• Horizontal stretch

What type of transformation is represented by G(x) = 0.25 * f(x)?

• Vertical compression

• Horizontal stretch

• Vertical stretch

• Horizontal compression