Exploring Function Transformations Vertically

The video tutorial covers function transformations with a focus on vertical shifts. It explains how vertical shifts affect the y-values of functions while x-values remain unchanged. The concept of parent functions is introduced, highlighting their basic nature centered around the origin. The tutorial provides examples of vertical shifts in equations and offers practice problems to reinforce understanding. It also includes multiple choice questions and graphing exercises to apply the concepts learned. Advanced examples demonstrate more complex transformations and vertex shifts.

If a point (2, 4) is translated 7 units down, what are the new coordinates?

• (9, 4)

• (2, -3)

• (2, 7)

• (2, 11)

What does the term 'parent function' refer to?

• A function with a vertical shift

• A function with a reflection

• A function with no transformations

• A function with a horizontal shift

If the vertex of y = x^2 is moved 2 units up, what is the new equation?

• y = x^2 + 4

• y = x^2 + 2

• y = x^2 - 2

• y = x^2 - 4

How do you represent a vertical shift of 3 units down in the equation y = x^2 + 3?

• y = x^2 + 3 + 3

• y = x^2 - 3

• y = x^2 + 6

• y = x^2 + 3 - 3

What is the new equation if the function y = x^2 + 3 is shifted 2 units down?

• y = x^2 + 1

• y = x^2 + 5

• y = x^2 - 1

• y = x^2 - 5

If f(x) = x^2 and g(x) is 4 units down from f(x), what is the equation for g(x)?

• g(x) = x^2 - 2

• g(x) = x^2 + 2

• g(x) = x^2 - 4

• g(x) = x^2 + 4

What is the shift for the function y = |x| - 10?

• 10 units up

• 5 units down

• 10 units down

• 5 units up

Omar graphed f(x) = x^2 - 3 and g(x) = x^2 + 2. How many units up is g(x) from f(x)?

• 6 units

• 3 units

• 4 units

• 5 units

If the vertex of f(x) = -3(x + 1)^2 + 2 is moved to g(x) = -3(x - 1)^2 - 5, how many units down is the shift?

• 5 units

• 6 units

• 7 units

• 8 units

Danette graphed f(x) = x^2 - 4x + 3 with a vertex at (2, -1). What is the new vertex if the function is shifted 3 units down?

• (2, -1)

• (2, 2)

• (2, -4)

• (2, -3)