Exploring Absolute Value Transformations in Algebra 2

The video tutorial guides students through graphing absolute value functions, starting with the parent function and moving on to transformations such as shifts, reflections, and narrowing. Students learn to create tables of values, graph functions, and analyze the effects of transformations on the parent function. The tutorial also covers writing equations for new graphs based on transformations, emphasizing understanding the impact of positive and negative values on graph behavior.

What is the parent function of the absolute value function?

• y = |x|

• y = x^2

• y = x

• y = 1/x

What are the coordinates of the points used to graph the parent function y = |x|?

• (0,0), (1,2), (2,4), (3,6)

• (0,0), (1,1), (2,1), (3,1)

• (0,0), (1,-1), (2,-2), (3,-3)

• (0,0), (1,1), (2,2), (3,3)

How does the graph of y = |x| + 1 compare to the parent function y = |x|?

• It shifts 1 unit down.

• It shifts 1 unit up.

• It shifts 1 unit to the left.

• It shifts 1 unit to the right.

What is the effect of adding 4 inside the absolute value function y = |x + 4|?

• The graph shifts 4 units to the left.

• The graph shifts 4 units down.

• The graph shifts 4 units up.

• The graph shifts 4 units to the right.

What are the coordinates of the points used to graph y = |x + 4|?

• (-5,1), (-4,0), (-3,1), (-2,2)

• (-5,0), (-4,1), (-3,2), (-2,3)

• (-5,2), (-4,1), (-3,0), (-2,-1)

• (-5,1), (-4,2), (-3,3), (-2,4)

How does the graph of y = |x - 1| + 3 compare to the parent function y = |x|?

• It shifts 1 unit to the left and 3 units down.

• It shifts 1 unit to the left and 3 units up.

• It shifts 1 unit to the right and 3 units up.

• It shifts 1 unit to the right and 3 units down.

What are the coordinates of the points used to graph y = |x - 1| + 3?

• (-2,5), (-1,4), (0,3), (1,2)

• (-2,6), (-1,5), (0,4), (1,3)

• (-2,4), (-1,3), (0,2), (1,1)

• (-2,3), (-1,2), (0,1), (1,0)

What happens to the graph of y = -2|x| compared to the parent function y = |x|?

• It reflects over the y-axis and becomes wider.

• It reflects over the x-axis and becomes narrower.

• It shifts 2 units to the right and becomes narrower.

• It shifts 2 units to the left and becomes wider.

What are the coordinates of the points used to graph y = -2|x|?

• (0,0), (1,-1), (2,-2), (3,-3)

• (0,0), (1,1), (2,1), (3,1)

• (0,0), (1,2), (2,4), (3,6)

• (0,0), (1,-2), (2,-4), (3,-6)

What is the new equation if the graph of y = |x| is shifted 4 units up and 2 units to the right?

• y = |x + 2| + 4

• y = |x - 2| + 4

• y = |x + 4| + 2

• y = |x - 4| + 2