Function Transformations and Effects

This video tutorial covers the transformation of linear functions, including horizontal and vertical shifts, reflections, and stretches. It explains the use of function notation and provides examples for each type of transformation. The video emphasizes understanding the 'recipes' for transformations and applying them to modify functions as required.

What is the primary focus of the video on transforming linear functions?

• Understanding function notation and transformation recipes

• Solving quadratic equations

• Graphing polynomial functions

• Learning about calculus

In function transformations, what does a positive horizontal shift indicate?

• A shift to the left

• A shift downwards

• A shift to the right

• A shift upwards

How is a reflection over the x-axis achieved in function transformations?

• By adding a constant to the function

• By multiplying the function by a negative

• By shifting the function horizontally

• By stretching the function vertically

What is the effect of a vertical stretch on a function?

• It shifts the function vertically

• It reflects the function over the y-axis

• It multiplies the function by a factor outside

• It compresses the function horizontally

If a function is shifted three units to the right, what is the new expression for the function?

• f(x) - 3

• f(x) + 3

• f(x - 3)

• f(x + 3)

What number represents a vertical shift of four units down?

• 4

• -4

• 2

• 0

How do you achieve a reflection over the y-axis?

• By multiplying the function by a factor

• By shifting the function vertically

• By adding a constant to the function

• By replacing x with -x in the function

What is the result of a horizontal stretch by a factor of two?

• The function is stretched vertically

• The function is stretched horizontally

• The function is reflected over the x-axis

• The function is compressed horizontally

What should you do after identifying the appropriate transformation recipe?

• Graph the function

• Solve for x

• Differentiate the function

• Find the values of H, K, b, or a