Function Transformations and Reflections

The video tutorial covers the transformation of functions, explaining the rules and notations used in transforming a parent function f(x) into a new function g(x). It includes examples of various transformations such as shifting left, right, up, and down, as well as reflecting across the x-axis and y-axis. The tutorial also demonstrates how to apply dilations, including stretches and compressions, to functions.

What is the notation used for a new function after transformations?

• h(x)

• f(x)

• g(x)

• k(x)

What does a negative sign in front of the parent function indicate?

• Reflection across the x-axis

• Reflection across the y-axis

• Vertical stretch

• Horizontal shift

If a function is shifted 2 units to the left, what will be the transformation inside the parentheses?

• x - 1

• x + 1

• x + 2

• x - 2

How do you transform a function to shift it down by 5 units?

• Add 5 to the function

• Subtract 5 from the function

• Multiply the function by 5

• Divide the function by 5

What is the result of shifting the function f(x) = 11x + 10 up by 3 units?

• 11x + 7

• 11x + 13

• 11x + 10

• 11x + 3

What transformation is applied to reflect a function across the x-axis?

• Multiply the entire function by -1

• Multiply the x variable by -1

• Add a negative sign to the function

• Subtract the function from 1

How do you reflect a function across the y-axis?

• Multiply the entire function by -1

• Subtract the function from 1

• Add a negative sign to the function

• Multiply the x variable by -1

What is the result of compressing the function f(x) = 2x + 3 by a factor of 5?

• (1/5)x + (1/3)

• (5/2)x + (5/3)

• (2/5)x + (3/5)

• (2/5)x + (5/3)

What is the scale factor for stretching a function if the factor is 10?

• Subtract 10 from the function

• Add 10 to the function

• Multiply the function by 10

• Multiply the function by 1/10

What is the final equation after stretching the function f(x) = -5x - 4 by a factor of 10?

• -50x - 4

• -5x - 4

• -50x - 40

• -5x - 40