Transformations of Absolute Value Functions

The video tutorial explains the transformations of the function f(x) = |x + 5| - 2. It covers vertical translation down two units and horizontal translation left five units. The tutorial demonstrates how to apply these transformations to the function and graph the result. It concludes with a discussion on the domain and range of the transformed function, highlighting that the domain is all real numbers and the range is y ≥ -2.

What is the parent function of f(x) = |x + 5| - 2?

• y = x + 5

• y = x^2

• y = |x - 2|

• y = |x|

How does the transformation f(x) = |x + 5| - 2 affect the y-axis?

• It shifts the graph left by 5 units.

• It shifts the graph right by 5 units.

• It shifts the graph down by 2 units.

• It shifts the graph up by 2 units.

What is the effect of the transformation inside the absolute value on the x-axis?

• It shifts the graph up by 5 units.

• It shifts the graph down by 5 units.

• It shifts the graph left by 5 units.

• It shifts the graph right by 5 units.

To apply a horizontal shift left by 5 units, what operation is performed on the x-coordinates?

• Add 5 to each x-coordinate.

• Subtract 5 from each x-coordinate.

• Divide each x-coordinate by 5.

• Multiply each x-coordinate by 5.

What operation is performed on the y-coordinates to shift the graph down by 2 units?

• Subtract 2 from each y-coordinate.

• Add 2 to each y-coordinate.

• Divide each y-coordinate by 2.

• Multiply each y-coordinate by 2.

What is the new x-coordinate for the point (-2, 2) after applying the horizontal transformation?

• -7

• 3

• 7

• -3

What is the new y-coordinate for the point (0, 2) after applying the vertical transformation?

• 0

• -4

• 2

• -2

After applying the transformations, what is the new position of the point (1, 1)?

• (-4, -1)

• (-6, 1)

• (-6, -1)

• (-4, 1)

What is the domain of the transformed function f(x) = |x + 5| - 2?

• All real numbers

• x ≤ 5

• x ≥ 0

• x ≥ -5

What is the range of the transformed function f(x) = |x + 5| - 2?

• y ≥ -2

• y ≤ -2

• y ≥ 0

• y ≤ 0