Exploring Transformations of Linear and Absolute Value Functions

This video tutorial covers transformations of linear and absolute value functions, focusing on translations, reflections, and stretches. It explains horizontal and vertical translations, reflections across the x and y axes, and how to perform vertical and horizontal stretches and shrinks. The tutorial also demonstrates combining these transformations and applying them in modeling scenarios, such as calculating profit from revenue.

What is the primary focus of the video?

• Quadratic functions

• Trigonometric functions

• Linear and absolute value functions

• Polynomial functions

What does a horizontal translation affect in the function?

• The y-intercept

• The h value

• The slope

• The k value

How do you translate a function 3 units down?

• Subtract 3 from the h value

• Add 3 to the h value

• Add 3 to the k value

• Subtract 3 from the k value

What happens to the function when it is reflected across the x-axis?

• The x-values become negative

• The entire function becomes negative

• The y-values become positive

• The function shifts to the right

In a reflection across the y-axis, what changes?

• The entire function becomes negative

• The y-values become negative

• The x-values become negative

• The function shifts up

What is a vertical stretch by a factor of 2?

• Multiply the x-values by 2

• Divide the entire function by 2

• Multiply the entire function by 2

• Divide the x-values by 2

How do you perform a horizontal stretch by a factor of 1/3?

• Divide the x-values by 3

• Multiply the entire function by 3

• Divide the entire function by 3

• Multiply the x-values by 3

What is the first step in a combination of transformations?

• Divide the function

• Perform the translation

• Multiply the function

• Perform the reflection

How do you calculate the profit if it is 50 dollars less than 90% of the revenue?

• Divide the revenue by 1.1 and add 50

• Multiply the revenue by 1.1 and add 50

• Multiply the revenue by 0.9 and subtract 50

• Divide the revenue by 0.9 and subtract 50

What is the profit for 100 downloads if the profit function is 1.8x - 50?

• $100

• $180

• $130

• $150