Exploring Transformations of Functions in Algebra 2

The video tutorial by Mr. Sullivan covers the basics of function transformations, including adding and subtracting constants to functions and their effects on graphs. It introduces parent functions like quadratic, cubic, and absolute value functions, and explains how transformations inside functions result in horizontal shifts that are opposite to what one might expect. The tutorial concludes with generalized rules for translations and practice problems to reinforce learning.

What happens to the graph of a function when you add a positive value to it?

• It shifts upward.

• It shifts downward.

• It shifts to the left.

• It shifts to the right.

If you subtract 4 from a function, what is the effect on its graph?

• It shifts 4 units downward.

• It shifts 4 units upward.

• It shifts 4 units to the right.

• It shifts 4 units to the left.

What is the shape of the graph of a quadratic function?

• A straight line

• A U-shape

• A V-shape

• A cubic curve

Which of the following is true about the graph of an absolute value function?

• It is a U-shape.

• It is a V-shape.

• It is a cubic curve.

• It is a straight line.

What happens to the graph of a function when you add a value inside the function (e.g., x + 4)?

• It shifts upward.

• It shifts downward.

• It shifts to the right.

• It shifts to the left.

When you subtract a value inside the function (e.g., x - 4), what is the effect on the graph?

• It shifts to the left.

• It shifts to the right.

• It shifts upward.

• It shifts downward.

What type of translation occurs when you add a value outside the function?

• No translation

• Diagonal translation

• Vertical translation

• Horizontal translation

How does the graph of a function shift when you add a value inside the function?

• It shifts in the opposite direction of the value added.

• It shifts upward.

• It shifts downward.

• It shifts in the same direction as the value added.

If a function is translated 3 units to the right and 2 units up, how would you write the new function in terms of the original function f(x)?

• f(x + 3) + 2

• f(x - 3) + 2

• f(x + 3) - 2

• f(x - 3) - 2

What is the new function if the original function f(x) is shifted 4 units to the left and 5 units down?

• f(x - 4) - 5

• f(x + 4) - 5

• f(x + 4) + 5

• f(x - 4) + 5