Function Transformations Explained

This video tutorial covers transformations of linear functions, focusing on how changes in the K value affect the graph. It explains vertical and horizontal shifts, reflections over the x and y axes, and introduces basic parent functions like linear, quadratic, and absolute value. The tutorial also includes practice problems to apply these concepts.

What is a parent function?

• A function that has been transformed.

• The simplest function with the defining characteristics of a family.

• A function that is always quadratic.

• A function that cannot be shifted or reflected.

What happens to the graph of a function when a positive value is added outside the parentheses?

• It shifts to the right.

• It shifts to the left.

• It shifts upward.

• It shifts downward.

How does subtracting a value inside the parentheses affect the graph of a function?

• It shifts the graph to the right.

• It shifts the graph upward.

• It shifts the graph downward.

• It shifts the graph to the left.

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CCSS.HSF.BF.B.3

What does a reflection over the x-axis do to the graph of a function?

• It flips the graph over the y-axis.

• It flips the graph over the x-axis.

• It shifts the graph to the right.

• It shifts the graph to the left.

Which of the following is the parent function of a quadratic function?

• y = |x|

• y = √x

• y = x^2

• y = x

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CCSS.HSF-IF.C.7D

What shape does the graph of an absolute value function typically have?

• A V-shape

• A straight line

• A U-shape

• A curve

How does adding a value inside the parentheses affect the graph of a function?

• It shifts the graph upward.

• It shifts the graph to the right.

• It shifts the graph to the left.

• It shifts the graph downward.

What is the effect of a negative sign outside the parentheses of a function?

• It shifts the graph to the left.

• It reflects the graph over the y-axis.

• It reflects the graph over the x-axis.

• It shifts the graph to the right.

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CCSS.HSF.BF.B.3

If a function is shifted up by 3 units, which of the following represents this transformation?

• f(x + 3)

• f(x) - 3

• f(x) + 3

• f(x - 3)

What transformation is represented by f(x - 2)?

• Shift right by 2 units

• Shift down by 2 units

• Shift up by 2 units

• Shift left by 2 units